An Apple Pie From Scratch, Part IVb: Planets and Moons: Size and Surfaces

DarinK

It’s all well and good to talk about events at a cosmic scale—galaxies and stars and century-long orbits—but human experience tends to happen within a very local sphere, and that will remain true long after we’ve made our way to other planets, and perhaps even other stars. Worldbuilding isn’t just about building big clockwork mechanisms—it’s also about building experiences.

So in this section I want to explore the question of “what would it be like to be on this planet?” I’ll tackle it with 3 approaches: First, the overall physical characteristics of a planet; Second, the many types of surfaces that a planet might have; and third, the appearance of other bodies and illumination from them on a planet’s surface.

• Physical Characteristics
• Size
• Solid Planets
• Waterworlds
• Gas Giants
• Other Size Parameters
• Temperature
• Surfaces
• Solid Surfaces
• Rock
• Metal
• Regolith
• Ice
• Carbon
• Sulfur
• Glass
• Vegetation
• Strange Matter
• Atmospheres
• Hydrogen
• Helium
• Nitrogen
• Oxygen
• Carbon Dioxide
• Carbon Monoxide
• Nitrous Oxide
• Water
• Hydrocarbons
• Halogens
• Sulfur
• Rock
• Others
• Oceans
• Water
• Hydrocarbons
• Sulfur
• Ammonia
• Carbon Dioxide
• Nitrogen
• Hydrogen
• Hydrogen Cyanide
• Alcohol
• Formamide
• Halogens
• Lava
• Others
• Alien Skies
• Calling in the Magratheans
• In Summary
• Notes

Back to Part IVa

Physical Characteristics

Size

Once we have our planets placed in orbits and their masses picked out, the obvious place to start in defining their characteristics is determining their size. For a planet of given mass, the radius will depend on the density, and the density depends on composition.

If you're in a hurry, you can roughly assume the composition from the mass, because the solid cores of planets tend to all be composed of a similar mix of rock and metal and there’s a good correlation between the mass of the solid core and the mass of the acquired hydrogen atmosphere, giving a simple mass-radius relationship.

Mass-radius trends (red line) with typical error (shaded regions) from known planets and exoplanets (symbols). Chen and Kipping 2016

Observed exoplanets can be divided¹ into three regimes of mass-radius relationships: Terrestrial planets up to 2.04 Earth masses with small atmospheres and high densities; “neptunes” between 2.04 Earth masses and 0.414 Jupiter masses with densities that drop rapidly with increasing mass due to larger atmospheres; And “jupiters” above 0.414 Jupiter masses with ever more massive atmospheres but radii slightly decreasing with mass due to greater compression of the atmosphere. We can therefore roughly predict the radius of a planet with any given mass: 

 

 

m = planet mass (Earth masses)

r = planet radius (Earth radii)

But if you have a little more time to work with and want a bit more accuracy, we can pick a specific composition and working out a mass-radius relation from there. 

Though there are many types of materials that could conceivably form planets, we'll simplify matters by dividing them into 4 broad categories, sorted from most volatile (tending to form low-density gasses or fluids) to most refractory (tending to form high-density solids with high melting temperatures):

• Hydrogen, referring specifically to the thick atmospheres of gas giants, though really this is typically a 3:1 mix of hydrogen and helium.
• Water, referring to water present as ice or a fluid on the surface of the planet, not mixed into other materials in the interior. Other volatiles like methane or ammonia may behave similarly, but have not been studied nearly as much.
• Rock, referring to lithophilic materials that tend to form oxides and appear in the mantle and crust. This is generally assumed to be mostly a mix of magnesium and silica (SiO₂), typically bridgmanite (MgSiO₃) or forsterite (Mg₂SiO₄).
  
• Metal, referring to siderophilic materials that tend not to form oxides and instead sink to form metal alloys in the core (this doesn't include all metal elements—some like magnesium, sodium, and aluminum are major lithophiles—just those that tend to be present as metal compounds). This is generally assumed to be mostly iron, with some nickel.

Some researchers also define another category, the chalcophilic materials that tend to bond with sulfur, but they’re a small portion of most planets, tend not to form distinct layers, and fall roughly between lithophiles and siderophiles in their properties.

On the surface, these materials have typical densities of 0.0001, 1, 3.5, and 7.8 g/cm³ respectively, but in the interior of a planet they can be highly compressed. Earth is about 2/3 rocky mantle and crust and 1/3 metallic core (even with large oceans and water mixed into the mantle, water only accounts for about 0.03% of the total mass), giving it an uncompressed density of just under 4.3 g/cm³, but the actual density is 5.5 g/cm³. For a given composition, more massive planets will have higher densities.

Marc Kushner, NASA GSFC

For planets less than about 0.01 Earth masses, bulk density will be close to uncompressed density (though you wouldn't expect to find any planets that small with much hydrogen). For larger planets, we can construct a mass-composition-radius relation in a number of ways that vary in complexity and accuracy.

Solid Planets

Terrestrial planets like Earth with a clear solid surface are the most straightforward, as we can ignore the atmosphere and other volatiles. This approximation² should be reasonably accurate for rock-metal planets between 0.01 and 100 Earth masses: 

 

R = radius (Earth radii)

M = mass (Earth masses)

f_r = rock mass fraction (where the rest of the mass is metal)

 

Predicted mass-radius relationships for rock-metal and water-rock planets. Fortney et al. 2007.

As a guideline, we have some reason³ to expect that Earthlike planets will generally form with core masses of about 15 to 40% of their total (rock mass fraction of 0.85 to 0.6 in the above formula), but Mercury has a core mass fraction of about 70% and we'll discuss the various ways a planet could lose much of its rocky exterior shortly.

There is some nuance here, of course. These models assume rock with a similar magnesium/silica mix as on Earth, but in truth the mix could vary⁴ and include substantial proportions of other materials like aluminum and calcium.  Even iron may, in some cases⁵, be oxidized and mixed into the rocky mantle during formation rather than forming a distinct core, resulting in a slightly less dense planet. But in general these issues shouldn't amount to more than a few percent variance in radius (though if you really want to explore them and you know a bit about python, it shouldn't be too difficult to do with ExoPlex, which can also handle waterworlds).

 

Mass-radius curves for planets with distinct iron cores and "coreless" planets with the iron mixed into the mantle; curves of the same color have the same bulk composition (aside from the pure planets). Elkins-Tanton and Seager 2008.

Finally, as we'll discuss, so-called carbon planets may have mantles of carbide rather than oxide minerals, and we can expect these to have similar densities, but they haven't been studied in as much detail.

Waterworlds

If there is a thick layer of water that comprises a significant portion of the planet's mass, things get a bit more complicated. First off, if the interior is mostly rock and the water at the surface is ice or liquid below the boiling point, then a simple mass-radius relationship is still possible²: 

 

R = radius (Earth radii)

M = mass (Earth masses)

f_w = water mass fraction (where the rest of the mass is rock)

As a general guideline, bodies formed of icy material from the outer solar system tend to form with around a 50:50 mix of water and rock, though much of the water can be later lost.

Incidentally, all these mass-radius relations so far are included in my worldbuilding spreadsheet; if you input a planet mass in the “system builder” tab, it will calculate radius using the simpler 3-regime model by default, but if you input metal or water mass fractions, it will assume the rest of the planet is rocky and calculate radius based on that.

However, if a waterworld has a significant metal core within its rocky interior, there is no such simple approximation. We can make a rough approximation by interpolating between the rock-metal and water-rock formulas (this is what the spreadsheet does if you enter both metal and water mass fractions), but if you need a more precise tool you can refer to the "Manipulate Planet" tool here.

But matters become even more complicated if the surface is warmed to above the boiling point. A large portion of the oceans may then evaporate into the atmosphere, further warming the surface through greenhouse heating in a runaway greenhouse effect. If the planet's surface gravity and water mass fraction aren't too large, this water may then all escape into space and leave the planet dry; otherwise, a long-lived steam atmosphere may form with no clear ocean surface below it (we'll discuss this in more detail shortly), something like a gas giant atmosphere. How large this atmosphere ends up being depends largely on its temperature, so now we have to deal with a mass-composition-temperature-radius relation.

Fortunately, this paper⁶ has worked through these factors: taking the mass fraction of the core out of the combined mass of the rock and core interior, rounded to the nearest 10%; the mass fraction of water out of the total mass of the planet, rounded to the nearest 10%; and the planet's equilibrium temperature (which I'll discuss shortly) rounded to the nearest 100 K, you can take the coefficients in the first file here⁷ and feed them into this formula:

 

R = radius (Earth radii)

M = mass (Earth masses)

a, b, c, d = coefficients from the link

e ≈ 2.718

The second file also contains a large number of pre-computed radii, and you can use the error codes to get a sense of the limits of these approximations for a particular composition; all should work up to 20 Earth masses, but are only reliable in the range with error codes of "0". Lower-mass worlds may be experiencing high rates of water loss that gradually reduces their water mass fraction.

Mass-radius curves for post-runaway waterworlds of different effective temperatures and water mass fractions (with pure rock interiors) compared to those for cool planets. Aguichine et al. 2021

Gas Giants

Much like these post-runaway waterworlds, the size of a gas giant atmosphere depends largely on the temperature. But determining a gas giant's temperature is a bit more tricky, as such huge bodies retain a lot of heat from formation and continue to produce more as the atmosphere contracts; Jupiter still produces substantially more heat than it receives from sunlight. There's a predictable decline in heating as the planet ages, but high amounts of solar heating can still have an impact, so we now have to deal with a rather thorny mass-composition-insolation-age-radius relation.

 

Fortunately, the authors of this paper⁸ have put together a model accounting for all these factors and released it as the python package planetsynth. It is a bit large for me to repackage as a standalone program, so here's a quick rundown on how you might go about using it:

• Install python and use pip to install the numpy and scipy packages.
• Download planetsynth from the above repository (under the green "code" button), unpack the zip file, and run setup.py.
• You can look at the instructions and examples on the repository or copy the script here which will run planetsynth with a short command-line prompt, taking the following parameters:
• Planet mass in Jupiter masses, with a range extending from a body about twice Neptune's mass to a small brown dwarf (the effect of early deuterium fusion isn't taken into account for the latter but this probably only matters for fairly young bodies).
• The bulk metallicity, representing the portion of the planet composed of something other than hydrogen and helium; this is assumed to be around 0.1 for Jupiter and 0.2 for Saturn.
• The metallicity of just the atmosphere, which should be roughly similar to that of the star; so around 0.02 for a sunlike star.
• The stellar flux, which can be calculated as 1367 * [star luminosity relative to sun] / [distance from star in AU]².
• The age of the planet in billions of years (up to 10 billion years, after which one can assume that the planet's evolution will be very slow).

This does leave us with a bit of a gap in determining the mass-radius relationship of smaller gaseous bodies like Neptune, but that probably varies greatly with composition so we needn't necessarily worry about being too precise there.

Other Size Parameters

Now that we have the radius, it’s easy enough to determine surface gravity and total surface area through the magic of ratios: 

g = surface gravity (Earth gs; 9.81 m/s²)

m = planet mass (Earth masses)

r = planet radius (Earth radii) 

A = surface area (Earth areas; 5.10*10⁸ km²)

r = planet radius (Earth radii)

XKCD

One other subtle effect is the distance to the horizon; the Apollo astronauts were reportedly surprised at how close it appeared on the moon. The exact distance depends on the altitude of the observer, local topography, and atmospheric refraction, but for the approximation of an observer on a perfectly spherical, atmosphereless planet:

d = distance to horizon (any unit so long as all 3 are the same)

h = height of observer

r = radius of planet

For an observer 2 meters tall, the distance to the horizon is 5.05 km on Earth and 2.64 km on the moon. 

Now, linking radius directly to density assumes that all planets are spherical. Fortunately this is generally a safe assumption because even solid materials behave like fluids at the size of planets and so will tend towards a hydrostatic equilibrium, with the surface deformed such that the gravitational pressure distributed equally across the whole surface, resulting in a sphere. The mass required for a planet's gravity to overcome the compressive strength of rock and force it into hydrostatic equilibrium is about 0.00035 Earth masses, but bodies as little as 0.00005 Earth masses—corresponding to a radius of about 250 km for rocky material—tend to be spheres as well⁹ because they were rounded by gravity when they first formed and partially molten and then were frozen into that shape as they cooled and solidified. Naturally these thresholds will vary, with less dense icy bodies tending to become spherical at even lower masses.

But even bodies well above this mass can deviate from spherical due to their rotation, which causes centrifugal acceleration that partially counteracts gravity (anyone who tells you centrifugal forces don't exist is a pedant who doesn't understand the regular use of mathematically convenient reference frames in physics). This results in an effective gravitational acceleration that's lower at the equator (which rotates fastest) than the poles (which remain static), such that the equator is less compressed and can bulge out further. The resulting oblate spheroid is shaped such that the combined gravity and centrifugal force still pulls directly "down" into the ground at all points on the surface, even though it varies in strength.

For most planets, this is a negligible effect: Earth is about 0.3% wider at the equator than between the poles; though Jupiter, which is larger and spins faster, has a 6.6% difference. But it can become significant for planets with extremely fast rotation. For such cases, the equatorial and polar radii can be estimated¹⁰ like so:

 

ϵ = ellipticity 

r = average radius (km)

r_e = equatorial radius (km)

r_p = polar radius (km)

d = density factor (where the interior can be approximated as having a density of [density at surface] * ( [distance from planet center] / [planet radius] )^-d ; d is ~1.09 for Earth and ~1.79 for Jupiter)

π  ≈ 3.14159

P =  rotational period (hours)

G = 5.166 * 10¹² km³ Earth mass^-1 hours^-2  

M = planet mass (Earth masses)

 

The previous formula for surface gravity will still hold at the equator, taking into account the increased radius, but it will now be counteracted by a centrifugal acceleration:

 

 

A = centrifugal acceleration (m/s²)

π  ≈ 3.14159 

r_e = equatorial radius (km)

P =  rotational period (hours)

(note the units here; to directly compare this to gravity in gs, multiply gravity by 9.81)

Gravity at the poles will be larger due to the lower radius, but not as much larger as you might expect because part of the planet's mass is now "above" the poles in terms of distance from the planet's center. It can be roughly estimated like so:

A_p = gravitational acceleration at poles (Earth g)

m = planet mass (Earth masses)

ϵ = ellipticity 

r = average radius (Earth radii)

 

(note again I switched back to g here—sorry if that's confusing—and that I'm using the average rather than polar radius because that makes the derivation easier)

 

If we play around with these numbers, we find that the combination of Earth's equatorial bulge and centrifugal acceleration only reduces gravity at the equator by less than 0.6%. If we shortened Earth's rotation period to 4 hours, the equator would bulge out by over 750 km relative to the poles and have an effective surface gravity of 0.8 g, while the poles would experience 1.03 g. At a period of 2 hours, it would bulge out by over 3000 km and experience only 0.17 g, while gravity at the poles rises to 1.13 g. At a period of about 1 hour and 50 minutes, centrifugal acceleration at the equator is equal to gravity; any faster and the planet tears itself apart (though the above method for estimating the equatorial radius may not hold close to this limit, so don't take this as an exact prediction).

Intense tidal forces can also stretch a planet from spherical, causing it to bulge out towards and away from the body inducing the tidal forces (rather than around the entire equator as for rotation). The tide height formula I gave in the last section should work as a rough approximation of the difference between the minimum and maximum radii of such a body, and the same approach as above should work for determining surface gravity at the tip of the tidal bulge (but the equation for gravity at the poles won't work).

Temperature

The surface temperature of a planet is another major factor determining both the composition and form of the surface, though it can be very tricky to work out.

A quick, easy way to get a rough estimate of a planet’s temperature is to track how total heat gained balances with heat lost: In essence, we assume that the planet gains heat from the sun based on its insolation—how much sunlight hits the surface on average, depending on the star's luminosity and the planet's distance from it—and albedo—what portion of this light is reflected directly back into space by the surface. The light not reflected is absorbed and warms the surface. This will cause the surface to emit thermal radiation into space, and, per the Stefan-Boltzmann law, increased temperature causes increased radiation. If the planet radiates more heat than it gains from sunlight, it should lose heat, cool, and so radiate less heat; if it radiates less heat than it gains, it should warm and radiate more. Eventually the surface should reach an average equilibrium temperature where the heat radiated matches the heat absorbed:

 

 

T_eq = equilibrium temperature (K)

L = star luminosity (relative to sun)

A = albedo (0.3 for Earth)

r = distance from star (AU)

This estimate works decently well for airless, rapidly-rotating bodies, and replacing the 4 with a 2 will give a decent approximation for the average dayside temperature of a tidal-locked planet. As an even quicker approximation, note that, for constant albedo, equilibrium temperature varies by 1/√(distance from star); so in general we should expect a planet at 4 AU from the sun to have about half the surface temperature of a similar planet at 1 AU. But albedo does vary (generally increasing with distance from the star as more ices form) so I'll try to give a sense of typical albedo values for each of the surface types we'll discuss shortly (at least where decent estimates are available; and note that albedo varies with the angle of the surface to sunlight, so the total albedo of the planet—the bond albedo—may not be quite the same as the numbers suggest).

But the real trouble comes from atmospheres, which can cause planets to behave differently from blackbodies. In particular, the greenhouse effect occurs when the atmosphere contains certain gasses, like CO₂, that are transparent to the short-wavelength sunlight that warms the planet but opaque to the infrared thermal radiation out from the planet, They thus reflect much of that heat back towards the surface and so effectively slow the overall rate at which the planet loses heat, causing the surface to warm to a higher equilibrium temperature. A combination of water, CO₂, and a few other minor gasses—totaling around 0.3% of the mass of the atmosphere—warms Earth in this way from an equilibrium temperature of 255 K to its current actual temperature of 288 K.

Some researchers will account for this by incorporating an emissivity value into the above formula, representing how much thermal radiation the planet emits compared to the ideal value estimated by the Stefan-Boltzmann law (for Earth it's around 0.6), but estimating the emissivity for a particular combination of atmospheric gasses can be devilishly complicated. Based on this paper¹¹, I've put together a process for estimating the greenhouse effect and the specific case of a roughly Earthlike planet with CO₂ and water as the dominant greenhouse gasses (though for reasons we'll discuss later we only need input a CO2 level and then we can assume this controls water vapor levels) and a resulting average temperature between 150 and 350 K, which I've added to the worldbuilding spreadsheet in the "Hab Planet Temp" tab.

The major downside here is that you need to set a specific albedo, whereas in reality the albedo should adjust with temperature as high-albedo ice forms or thaws. I may someday attempt to construct a more complex model like the one-dimensional energy balance model described in the paper that accounts for varying ice cover and seasons, but that will have to wait for another day.

Past that, there aren't really any usable tools for a broader range of greenhouse gasses. The closest thing I can find to something usable is HELIOS and that is a very generous way to describe it. So don't be afraid to settle for a very vague estimate based on the equilibrium temperature and a generous fudge factor.

As a final note, planets can receive heat from sources other than sunlight, most notably geothermal heat from the interior. I've already mentioned that internal heating can be a significant factor for gas giants (and planetsynth will determine effective temperature with this in mind), but with smaller, solid planets it's less of a concern; Earth's surface receives less than 0.04% of its total heat from the interior. Jupiter's moon Io, far from the sun and riven by volcanism caused by its intense tidal heating, still gets only about 1/5 of its heat from its interior. Even warming small areas with geothermal heat is a tall order: the Antarctic volcano Mount Erebus is one of the few places in the world receiving enough persistent heating to maintain an open lava lake, and yet is still covered in ice up to the rim of its crater. Still, as we'll discuss another time, even this small amount of heat can warm a planet to Earthlike temperatures on its own if there's a thick-enough atmosphere of greenhouse gasses to trap it in.

Surfaces

Classifying planetary bodies purely by broad characteristics, while informative in a pinch, is a bit too simplistic. If we want to know what a planet will actually be like to visit and live on, then what we really have to ask is what sort of surface we will encounter—and how many surfaces, for planets with distinct atmospheres, oceans, and landmasses. To some extent this is determined by size as well, but there’s a lot of variation, both observed within our solar system and theorized elsewhere.

A lot of fictional depictions have a bad habit of depicting single-biome planets that are homogenous across their surfaces. It is feasible for a planet’s surface to be dominated by rock, ice, water, or lava, and to some extent a desert world is possible, but as more complexity is added (atmospheres, oceans, tectonic activity) it will tend to lead to more surface variation. Even Mars, a prototypical desert planet, has rocky highlands, dusty lowlands, ice caps, and various local features formed by volcanoes, glaciers, tectonic forces, and water. I would expect any planet with complex life to have a very diverse surface. Unfortunately, though, for many types of possible planetary surfaces we can only broadly speculate.

Let’s take a quick tour of some of the more common types of surfaces—solid, liquid, and gaseous—that we might expect to encounter.

Solid Surfaces

Rock

This is the obvious one, but of course there are all sorts of different kinds of rock. For a system with a composition like ours, rocky material consists mostly of silica (SiO₂) mixed with magnesium, calcium, and aluminum, though many other elements appear in varying portions, including some volatiles and siderophiles like iron.

NWA 3189 Meteorite cross-section in closeup. James St John, Wikimedia

The first rocky material formed would have been chondritic, named for the round chondrules, formed from droplets of material that was briefly molten during accretion, that make up much of its mass. Many asteroids are still chondritic today. Color varies and albedo of these bodies is typically 0.3-0.6, and density is around 3.5 g/cm³.

Basalt. Wikimedia

Once enough mass has gathered together to form a planet, even a small one, the heat of formation and internal radioactivity will usually cause the originally chondritic material to melt and differentiate. Once the surface cools, it will usually form mafic rocks (so-called because they're relatively rich in magnesium and iron, a.k.a. ferrum), primarily basalt, a grey or black and frankly visually uninteresting rock. Much of the initial basalt surfaces of our solar system have been ground up by impact events, but later tectonic activity can cause lava to flood over the surface, forming flood basalts that are still visible as the dark regions on the Moon and Mars. Earth has some flood basalts, such as in Iceland, and the ocean floors are primarily mafic. Albedo is low, around 0.1, and density is 3.0 g/cm³ due to differentiation out of some of the metals.

Varieties of granite. Jstuby, Wikimedia

On Earth, tectonic processes cause volatiles to mix with mafic rocks in the upper mantle at subduction zones, and the resulting magma rises up through the crust to form felsic rocks (so-called because they're rich in feldspar, a sodium/potassium/calcium-aluminum silicate, and silica), primarily granite at first, but later tectonic activity can form many other igneous and metamorphic rocks with broadly similar properties. The rocks are even poorer in metals than mafic rocks, lending them a light grey or white color, or reddish due to alkali metals, and a higher albedo of around 0.3. They're also less dense, around 2.5 g/cm³, which causes felsic masses to “float” higher on the mantle, forming our modern continents.

Though felsic rocks on Earth are mostly associated with plate tectonics, Mars also has regions of felsic crust, and some felsic rocks may even exist¹² on Venus. Typically this requires continuing volcanism in the presence of water, but other volatiles like chlorine or fluorine may work as well.

Sandstone. Ester Inbar, Wikimedia

And finally, planets with atmospheres experience various weathering processes that break down mafic or felsic rocks and rework the material into sedimentary rocks. Quartz (near-pure silica) will resist erosion longest, and so survive as intact grains that can be cemented together to form white or yellow sandstone. Other materials are dissolved and later deposited as carbonate, sulfate, phosphate, or nitrate minerals, with varying colors, albedos, and densities—though all usually broadly similar to felsic rocks. Evaporation of large bodies of water can leave behind evaporites like halite and gypsum that appear mostly white and have albedos as high¹³ as 0.7. Earth and Mars both have large regions of sedimentary rocks, while Venus’s lack of water and frequent volcanic resurfacing seem to largely preclude their formation.

There is some evidence⁴ that rocky exoplanets could have compositions unlike any in the solar system, particularly varying in the ratio of silica to magnesium. Silica-rich planets could potentially form fully felsic crusts with more quartz, which might be more buoyant¹⁴ (especially if rich in sodium as well) and so less prone to subduction and plate tectonics—though it's hard to be sure given the complexities and uncertainties of global tectonics (something we will discuss a little more in the next few posts). On the other hand, more magnesium-rich planets may form crusts of ultramafic rocks like green serpentinite (albedo ~0.3) that are rich in olivine (~0.2).

 

Small, dry worlds like the moon may initially form¹⁵ with a crust of almost pure feldspar. On the moon, this is predominantly grey anorthosite, but there are red, blue, and yellow feldspars as well; whether any of these could plausibly dominate the crust, I'm not sure. Later volcanism will tend to replace this with basalt, but the moon still retains it in substantial highland regions. Though this forms with an initial high albedo of around 0.6, weathering by solar wind can reduce it to around 0.2; even a thin atmosphere can prevent this, but a small, volcanically inactive world is unlikely to retain one.

 

There are a few other types of rocky planet compositions that are not considered particularly likely but are worth mentioning just to be thorough; though the geochemistry here is a bit complex and hasn't really been rigorously explored so don't put too much trust in my specific predictions:

• Material at the inner edge of the protoplanetary disk might be heated enough to vaporize away sodium, magnesium, and iron, leaving it relatively enriched in aluminum and calcium. A planet formed from this material¹⁶ might lack an iron core and would have a crust rich in reddish (though occasionally yellow or green) garnet, and probably also higher levels of variously colored corundum (which includes red ruby and blue sapphire) and perhaps green epidote and jadeite and blue kyanite. The surface may thus be more colorful overall, with perhaps a reddish tendency, though duller augite, albite, and nepheline may be more common as well. A calcium-rich crust might also form more carbonates, pulling CO₂ from the atmosphere, which might make these planets relatively cool if they appear in the habitable zone.
• One possibility I'll bring up a few times in this post is that a white dwarf may be broken apart by a close encounter with a neutron star or other massive object, forming smaller planets. If this occurred with an oxygen/neon/magnesium red dwarf, the resulting planet should form a solid interior of mostly white or green periclase, though the likely presence of carbon may complicate matters and the planet may have a very deep Ne/CO/O₂ atmosphere, at least initially.
• Titanium is a common secondary element in rocky crusts, and though there's no particular expectation that it might become more dominant, if it did we might expect more dark ilmenite, red or green titanite, and red, brown, or yellow rutile, famous for its tendency to form long, thin crystals.

Metal

Iron is by far the most abundant metal in the solar system—and the universe—with nickel a distant second (to be clear, I'm referring to "metal" in the chemical sense—elements on the left of the periodic table that tend to form metallic bonds—rather than the astrophysical sense used in the previous posts). Thus, all rocky bodies in the solar system have iron-nickel cores (though as mentioned, a planet could conceivably lack a core⁵ if all its iron is oxidized during formation, causing it to be mixed in with the rocky crust). Differentiation during planet formation will typically place metals under layers of rock and volatiles, so exposed metal surfaces are rare, but there are a few plausible ways they might develop.

Iron meteorite; the hexagonal crystal patterns form naturally from molten iron in low gravity. Tila Monto, Wikimedia

First, interactions between sunlight and dust particles¹⁷ at the inner edge of a protoplanetary disk may preferentially push silicates outwards and leave iron behind, allowing metal-rich planetesimals to form. This could be the cause of Mercury’s high metal content of around 70%, as well as the origin for exoplanets¹⁸ that must necessarily have high densities to orbit as close to their stars as they do (because of Roche limit restrictions). Even more metal-enriched bodies, sometimes termed vulcanoids, could exist in close orbits of the sun near 0.1 AU, but none have been observed¹⁹—though the interference of the sun’s glare makes it hard to rule out the presence of small asteroids. However, this is unlikely to produce a body completely devoid of rock.

Concept of Psyche. Maxar/ASU/P. Rubin/NASA/JPL-Caltech

But if a planet is large enough to differentiate, a sufficiently powerful impact could strip away the rocky exterior of a differentiated body, exposing the metal core; this is another proposed origin²⁰ for Mercury as well as the metal-rich m-type asteroids. The largest such asteroid, Psyche, at 0.000006 Earth masses, may be almost pure iron-nickel, at least on the surface. Attaining such high metal content from impacts becomes more difficult for larger bodies, as the higher gravity prevents escape of the ejected material, but it may still be possible²¹ to attain bodies of over 90% iron with extremely high-velocity impacts. The rock need not be completely removed; once the rocky exterior thins down to 30 km or so, sulfur-rich iron-nickel magma can erupt²² through the crust and coat the surface.

Alternatively, a planet or moon that passes inside its Roche limit may have²³ its outer layers more completely stripped away. A planet in a very close orbit may also have its rocky exterior gradually vaporized by intense heating from the star.

 

However they form, metal-rich planets will be very dense, around 8 g/cm³. Pure metals tend to be grey or silver in color and have very high albedos, but in most cases the surface will likely be composed of metal oxides or sulfides with albedos around 0.1-0.2 and red, black, or other colors.

In addition to exposed cores, a metal-rich layer could conceivably form on top of rocky crust in a few different ways¹⁵:

• A planet that initially forms with a substantial hydrogen atmosphere may have some rocky materials mixed into that atmosphere as vapor; if the atmosphere is then lost to atmospheric escape, these may then deposit as layers, with sodium possibly depositing last to form a layer of silvery, high-albedo metal.
• An extremely oxygen-rich atmosphere may form large amounts of red or black iron oxide (albedo ~0.2) on the surface, similar to Mars.
• A hot atmosphere rich in water or CO₂ could leech metals from the crust and deposit them as minerals like pyrite (FeS₂, goldish in color, albedo ~0.1). This may have occurred²⁴ on some highland areas of Venus.

Regolith

This is a broad term describing any loose material over the solid crust. So it applies to soil and sand on Earth, the ultrafine dust of Mars, and the surface material of the moon (in principle it could apply to snow as well, though it's rarely used that way). On Earth and Mars it’s produced by the weathering of solid rock by wind and water, but on airless bodies it can be produced by the continuous bombardment of micrometeorites grinding up the surface; even many asteroids are covered in regolith.

Left to right: Earth soil (HolgerK, Wikimedia), Lunar regolith (NASA), Martian regolith (NASA/JPL-Caltech/MSSS)

The moon Titan also appears²⁵ to have regolith formed of tholins (a mix of molecules formed by combinations of nitrogen and hydrocarbons) that form in the atmosphere, deposit on the surface, and then are eroded by methane rains.

Regolith types can be broadly defined by the composition and size of the average grain, but our grain size types are calibrated for Earth, where moisture will tend to bind small grains into larger ones; on drier bodies the regolith can continue to break down into ever-smaller grains, which could be a health and mechanical hazard for any future settlers of the moon or Mars. A typical sand grain in a desert on Earth has around 100 times the diameter of a grain of Martian soil, putting the latter in the range of “clay”, though it is much less cohesive than Earth’s clay. In spite of the difference, dunes have been observed on Earth, Mars, and Titan, indicating that under the influence of similar forces all types of regolith tend to form similar structures regardless of composition.

Regolith is produced all across Earth, but most is either washed out to the oceans by water or held in place by vegetation. Sandy deserts are caused by an absence of moisture, which leads to an absence of vegetation, and a lack of static surface material also exposes more bedrock for weathering. Because this sand is, as mentioned, primarily silica, the albedo can be as high as 0.4 in dry conditions. Martian iron oxide dust has an albedo around 0.3, and lunar regolith is close to basalt, around 0.12. Broadly speaking, all regoliths should be lighter colored than their source rocks.

Ice

Water ice is the typical surface material for small bodies in the outer system, but past their respective icelines ammonia (NH₃), methane (CH₄), nitrogen (N₂), and carbon monoxide (CO) ice can form as well.  In the solar system, water is the dominant component of all icy bodies that have received close study, but many appear to have some ammonia and methane as well, Triton and Pluto both have layers of nitrogen covering parts of their surface, and Mars has large amounts of CO₂ ice in its southern ice cap. As we'll discuss, more carbon-rich exoplanets are conceivable, forming predominantly CH₄, CO₂, or CO ices. A near-pure CO planet might conceivably form²⁶ from breakup of a white dwarf.

The iceline for water is estimated to have been around 2.7 AU during planet formation and is 5 AU currently in our solar system, but for other compounds it’s harder to pin down: For nitrogen²⁷ and ammonia it’s somewhere inside Saturn’s orbit at 9 AU, for methane it’s inside Uranus’s orbit at 18 AU, and for CO²⁸ it’s around 30 AU. But the iceline is not a hard limit; many asteroids that formed outside the primordial iceline but inside the current iceline have surface layers of dust that protect icy interiors. Inside the primordial iceline, ice-dominated bodies are unlikely to form, but comets could deliver at least some ice and this could survive in permanently shaded craters or valleys near the poles of a planet with low axial tilt. Tidal-locked worlds can have ice covering their nightsides even in very close orbits, and for cool atmospheric worlds this may extend into the dayside, forming an “eyeball world” with ice ringing the warmer center of the dayside.

Concept of TRAPPIST-1f. NASA/JPL-Caltech

An atmosphere will raise the melting temperature of ice, hence the ice caps of Earth and Mars well inside the iceline. This can work even for fairly small bodies; were an icy body like Ganymede or Europa to migrate into the inner solar system, some of the surface ice would sublimate to form an atmosphere of water vapor. As we'll discuss shortly, much of this water would escape into space, but these bodies have a lot of water to lose. As such, they can survive²⁹ with an icy surface for billions of years in orbits as close as 1.1 AU.

Ice has a lower compressive strength than rock, so it generally can't form steep mountains like rocks. Once more than about 50 meters of ice piles up (given Earthlike gravity) it will form a glacier and flow outwards in all directions unless channeled by rocky features. Glaciers can be 10s of kilometers thick in their centers, but have very shallow slopes. If the ice layer is relatively thin (less than 100s of kilometers) and is underlain by a liquid ocean, the surface will be even smoother because any topographical features are unsupported. Smaller bodies with weaker gravity may have more dramatic features, like the 20-km high cliffs of Miranda.

It’s easy to think of an ice-covered world as frozen and dead, but they can be remarkably dynamic. Many of the icy worlds of our solar system show evidence of cryovolcanism, where heat from the body’s interior causes water to burst through the overlaying ice just as lava bursts through the crust on Earth. Repeated warming and cooling of the ice can also cause sections of the surface to rift apart and slide past each other. On Europa these rifts may even³⁰ divide into tectonic plates that subduct under each other, just as rocky plates do on Earth.

NASA/JPL-Caltech

Triton, Neptune’s largest moon, has a surface layer of transparent nitrogen ice that causes a sort of “solid greenhouse effect” under sunlight, heating darker subsurface ice until it melts and bursts through the surface to form geysers that could last over a year³¹ and shoot up plumes of material 8 km high. Triton also shows evidence³² of cryovolcanism and tectonic rifting, and some flat plains appear to have been formed by floods of cryolava of water and liquid ammonia, analogous to the flood basalts of inner system bodies. Similarly, large regions of Pluto's surface have been replaced³³ with cryovolcanic activity within the last few hundred thousand years.

Antonio Cicolella, Wikimedia

Fresh snow has a very high albedo of 0.8, but partially melted and refrozen ice will typically be closer to 0.6, and “dirty ice” mixed with regolith can be as low as 0.2. These values will all be lower for planets orbiting redder stars. Micrometeorite impacts should tend to gradually coat a planet’s surface with a dusty layer, lowering the albedo, but cryovolcanism and related resurfacing processes can keep the surface covered in fresh ice. Pure water ice is, of course, white or bluish, but methane and nitrogen are more pink, and the ice may be covered by brown or grey dust, red or black tholins formed in a tenuous atmosphere, or byproducts of native life that might be a variety of colors³⁴. 

Carbon

Most of what I’ve said so far has assumed a primarily oxide chemistry: a silicate       and metal oxide mantle, water seas, and what little carbon there is mostly forming carbonate minerals and CO₂. This is because early in a system’s development, carbon and oxygen form carbon monoxide (CO), a volatile that is then largely driven out of the inner system by solar wind. Our solar system has a carbon/oxygen (C/O) ratio of 0.5—which should be typical³⁵ of most nearby systems—so formation and then loss of CO from the inner system consumed most carbon but left plenty of excess oxygen.

 

However a system with a C/O ratio above 0.8 could retain much more carbon relative to oxygen, causing the formation of carbon planets. Individual carbon planets could also conceivably form in otherwise carbon-poor systems due to local variations³⁶ in the composition of the protoplanetary disk.

Concept of carbon planet. Luyten, Wikimedia

Such a planet³⁷ would be dominated by carbide chemistry: a silica carbide and diamond interior, graphite surface, hydrocarbon seas, and an atmosphere likely dominated by some mix of hydrogen(H₂), light hydrocarbons like methane(CH₄), and carbon monoxide (CO) or carbon dioxide (CO₂). Tectonic processes could bring some of the mantle material to the surface, meaning these planets could have literal mountains of diamond. However, carbides and diamond are poorer insulators³⁸ than oxides and likely mix less with heat-producing radioactive materials, so these planets will cool faster and probably be tectonically inactive for most of their lives (if not provided with an additional energy source like tidal heating).

Some planets could also have a mix of oxide and carbide chemistry. If large amounts of water are added to a carbide planet in the later stages of formation, it could oxidize the outer layers³⁹, forming a silicate crust like Earth and a diamond and silica upper mantle; later volcanism could bring some diamond and carbides to the surface, forming an odd mineral mix, and would likely produce large amounts of atmospheric hydrogen and methane as a byproduct. Conversely, carbon may fail to replace oxygen in the mantle during formation and instead⁴⁰ form a layer of graphite (and, if deep enough, diamond) over a silicate mantle. Graphite could also precipitate out⁴¹ of a hot (>400 K), hydrocarbon-dominated atmosphere, accumulating on the surface.

It’s hard to judge what the exterior appearance of a carbon a planet would be, and really it could be as diverse as for oxide planets. Graphite is very dark grey or black with an albedo of 0.04 (though it may be higher over the surface of a whole planet with light hitting it at various angles), but diamond can have a range of colors and much higher albedo (I can’t seem to find a specific number because most people have, for understandable reasons, never considered the possibility of extensive regions of diamond on a planet’s surface, but I’d expect it to at least be comparable to quartz). But there is a huge range of minerals that are seen nowhere on Earth but could conceivably form in a carbon-rich, oxygen-poor environment, ranging from carbides⁴² that should behave much as we expect "rocks" to, with high melting points and stable chemistry, to various organic materials⁴³ that might more resemble tar, plastics, or other synthetic polymers, and we know very little about which of these specifically would be geologically favored.

Sulfur

Sulfur is a bit of an odd element; more volatile than silicate rock and more refractory than water, but not quite common enough to dominate the chemistry of the protoplanetary disk like O, C, Si, and Fe do. On Earth the vast majority of the initial sulfur content sank towards the core and has remained there, leaving the crust depleted of it, and much the same is true of most other solid bodies. The exception is in volcanic regions where sulfur dioxide (SO₂) is released into the atmosphere and concentrated deposits of elemental sulfur can form. If these minerals aren’t soon buried, they will be weathered by water and form sulfide or sulfate minerals downstream, in effect diluting the sulfur in the silicate crust.

Image of Io. NASA/JPL/University of Arizona

On Io, however, constant widespread volcanism releases huge amounts of sulfur and there is no water to weather it. As such, Io is covered by broad expanses⁴⁴ of yellow and red elemental sulfur and white SO₂ ice, with an average albedo of 0.63. Any world with an Earthlike composition that experienced similar rates of volcanism for an extended period (which would require high internal heat, probably only possible from tidal heating by a star or planet in most cases) could expect similar results. At higher temperatures, sulfur and SO₂ will evaporate or melt, but there may still be an abundance of sulfide or sulfate minerals like yellowish pyrite (FeS₂), white gypsum (CaSO₄·2H₂O) and baryte (BaSO₄), and orange alunite (KAl₃(SO₄)₂(OH)₆).

Glass

Obsidian glass forms when magma cools so rapidly that it cannot form crystals. This happens occasionally on Earth and some other solar system bodies, usually forming small fragments, but some researchers have suggested⁴⁵ that rapid cooling of magma oceans on exoplanets could form large surfaces of smooth glass. It would typically be black or grey depending on the composition and, contrary to what you might expect, have a low albedo of 0.1-0.2.

Vegetation

Obviously I can only speak with confidence about Earth’s vegetation, but it might be broadly similar for other worlds. Contrary to many fictional depictions, it’s not realistic for a planet to be entirely covered in thick forest. Vegetation requires water, and a planet with enough water to support widespread forests will also likely have large oceans. Perhaps we could posit floating vegetation spreading onto and eventually dominating the sea, but that raises questions about nutrient supply and tolerance of extreme ocean storms. A flat “swamp world” with global but shallow water coverage isn’t realistic either: For one, there would be no nutrient-rich mountains or major river systems to supply these forests; for another, such a world would have to be tectonically dead, which doesn’t bode well for its long-term habitability. At any rate, any habitable planet is going to have global weather systems that lead to wetter and drier regions, and so forest cover should at least have some regional variation.

But where vegetation occurs, it should be abundant. It’s easy to forget that the temperate regions of Earth that are now dominated by urban areas and agriculture had near-total forest coverage before human activity, and this has been the case most of the time since the Carboniferous Era. Before then, simpler plants and mats of microbes were also likely widespread.

On Earth, the albedo of vegetation is around 0.15, lower for thick forests and higher for grassland. How it might vary and in particular how plant color might evolve under different stars is a subject we'll have to explore in depth another time. On Earth, photosynthetic life is predominantly green but can also be found in red, blue, and purple varieties. Life exposed to stronger UV radiation might also evolve⁴⁶ fluorescent pigments for protection, absorbing UV and emitting it as visible light.

Strange Matter

Some researchers believe⁴⁷ that the high pressure inside neutron stars may produce strange quark matter, composed of condensed quarks rather than distinct protons, neutrons, and electrons. Collisions between neutron stars could then tear away pieces of this strange matter, producing strange dwarfs with masses similar to small stars or even strange planets. If the strange matter remains stable outside the pressure of a neutron star, these objects could be astoundingly dense, over 400 trillion g/cm³, compared to the 1-10 g/cm³ we expect of planets of normal matter. Alternatively, if the strange matter is not stable, it may decompress⁴⁸ into strangelet crystals (I could not even begin to guess what these would look like), resulting in a maximum density of a mere 1 trillion g/cm³ or so and a minimum density of under 10,000 g/cm³.

Possible mass-radius relations for compact strange matter stars and relatively "diffuse" strangelet crystal planets. Alford et al. 2012

A strange planet could also⁴⁹ form a crust of normal matter. Because this crust will be far less dense than the strange matter, even at the extreme pressure at the boundary between them, a large range of densities is possible, down to under 30 g/cm³ (though only at certain masses); so, for example, a strange-matter-core planet could have 1/4 Earth's mass and 1/3 the radius, for a surface gravity about twice as strong.

 

Possible mass-radius relations for planets with a strange matter core depending on the density at the base of the normal matter crust. Kuerban et al. 2020

Similar modelling has not been done for a normal matter crust over a strangelet crystal core, which may allow for even smaller planets of moderate gravity. It may also be possible⁵⁰ for strangelets and normal atoms to form crystals together, which would presumably have some intermediate density. A planet with a radius of 100 km, for example, would need a bulk density of 400 g/cm³ to have the same surface gravity as Earth, which may be achievable with some combination of these materials (though before you get too excited, the escape velocity of such a planet would be too low to retain much of an atmosphere).

In any case, such high densities would give these planets very small Roche limits; a strange planet could potentially orbit a neutron star at a distance of under 100 km, with an orbital period of under 1 minute.

But it's worth emphasizing again that the existence of strange matter and its stability outside a neutron star (or that of strangelet crystals) is still speculative, and much uncertainty remains over what exactly the properties of such materials would be.

Atmospheres

Every planet has at least some thin gas near its surface, but here I’m concerned mostly with thick atmospheres that can significantly impact the chemistry of the solid surface and allow for liquid oceans. As a planet forms, it will typically form a primary atmosphere from either gasses accreted from the surrounding protoplanetary disk (moreso the case for gas giants) or gasses released from the initially molten surface (moreso smaller planets). But as planets age and evolve, there are a variety of processes that can cause gasses to be gained and lost; Earth's modern atmosphere bears little resemblance to the one it likely first formed with.

To start off, volatiles mixed into the crust or deeper interior during formation can be outgassed into the atmosphere by volcanic activity, which is the primary way by which atmospheres gain gasses. The gasses produced depends on the chemistry of both the interior and the crust that magma passes through on its way to the surface, the latter of which especially may change as the planet ages and evolves; Earth's volcanos, for example, produced large amounts of H₂ and CH₄ when the planet was young but have now shifted more towards CO₂ and SO₂ (with water more consistently produced throughout). The overall rate of outgassing will also decline as the planet ages, the interior cools, and volcanism decreases; but this is only the general trend over billions of years, with plenty of shorter-term variation.

Once outgassed, whether or not these gasses remain in the atmosphere depends in large part on the climate; if the surface is cold enough, some gasses may condense to a solid or liquid form. Even if this only occurs on a small portion of the surface, the gas circulating over the surface will continue to collect in this cold trap. As atmospheric pressure drops, this may reduce greenhouse heating or heat flow across the surface, expanding the cold trap and potentially leading to total collapse of all or part of the atmosphere onto the surface. This can sometimes be avoided if the accumulated solid or liquid can flow out of the cold trap into a warmer region; as mentioned, even solid ice will flow once more than ~50 m deep, forming glaciers that tend to reach an equilibrium between melting at their edges and freezing and snow accumulation in their interiors. And, of course, a warming climate may instead melt or evaporate previously trapped volatiles.

Gasses can also react chemically with each other, forming new compounds and consuming others. We'll have to dig a bit deeper into the chemistry at some other point, but for now note that atmospheric gasses (or any materials really) can be classified as oxidizing, tending to strip away electrons from other compounds, or reducing, tending to give away electrons, or anywhere in a spectrum in between; oxygen is a common oxidizer and hydrogen and carbon are common reducers. Strong oxidizers and reducers will react with each other until only one remains, so you would not expect to see an atmosphere containing large amounts of both oxidized (O₂, NO₂, SO₂) and reduced (H₂, CH₄, NH₃, HCN) gasses at the same time, though small amounts of these gasses could be appear in a hostile atmosphere if some process is consistently producing them. Some gasses are more inert (N₂, Ar), and compounds of both oxidizers and reducers will tend to cancel out to produce inert gasses (H₂O, CO₂, CO), so these can exist in any but the most oxidized or reduced atmospheres (though their formation may be more favored under one or the other condition).

Strong oxidizers and reducers will often react spontaneously (though this depends somewhat on temperature and concentration) but reactions between more stable materials can be helped along by catalysts (often metals) on the surface or external sources of energy; high-energy photons in sunlight or other radiation sources may cause photolysis, breaking apart gas molecules into often less stable products that may then recombine in new ways or react with other gasses. And, of course, life may metabolize gasses to extract energy or nutrients and then expel different gasses as waste.

The compounds produced by these reactions may or may not have different malting and vaporization temperatures and so could condense out of the atmosphere. Gasses can also react directly with materials on the surface, often sequestering them in the crust by converting them to solid minerals that may then be buried. But the materials they react with are consumed as well, so these crustal "sinks" may eventually become saturated if all the material has reacted and so no more gas can be consumed. Volcanic activity can produce new unsaturated crust to consume more gasses, but at the same time the same volcanism and tectonic processes (especially subduction that pulls surface minerals into the hotter interior) can break down minerals in the crust and release the sequestered volatiles. CO₂ in particular exists in Earth's atmosphere in an equilibrium between rapid sequestration and outgassing.

 

More permanent is loss of atmospheric gasses to space, from where they cannot be recovered. In most cases the most important mechanism for this will be thermal escape. Any gas in an atmosphere will have some average velocity based on its molar mass (a measure of the relative mass of different types of molecules) and temperature:

v_therm = typical thermal velocity (m/s)

R = gas constant; 8,314.4598 g m² s^-2 K^-1 mol^-1

T = temperature (K)

m_mol = molar mass (g/mol)

If the average thermal velocity at the exobase—the region at the top of the atmosphere where gas particles can potentially reach  space without bouncing off other particles—is close to the planet's escape velocity—which, you may recall, is determined by the planet’s mass and radius—then the planet experiences hydrodynamic escape, where the gas simply flows off the planet like a continuous wind. Escaping lighter gasses can carry away heavier gasses with them, removing the entire atmosphere. This appears to be happening to hot jupiters in other systems, and Earth and Venus may have⁵¹ lost their primary hydrogen-rich atmospheres this way.

But even where the average velocity is below escape velocity, random collisions will cause some gas particles to greatly exceed the average, so escape velocity needs to be⁵² at least 2-3 times the average velocity at the exobase to prevent hydrodynamic escape, and even if it's higher all atmospheres still lose some gas due to Jean’s escape. The general rule of thumb is that when the  average velocity of a gas reaches 1/6 the escape velocity, then the rate at which it escapes will be great enough that the atmosphere could become depleted of that gas in less than billions of years. The exact threshold will vary because of complexities in how gasses distribute in the atmosphere and the potential for outgassing to compensate for losses, but much beyond this limit and the gas will escape far faster than any production process can compensate for—save perhaps for brief episodes where a large impact or volcanic event suddenly releases large amounts of gas, which could then take millions of years to escape (the same for if an atmosphere is added artificially during a terraforming process).

Rough chart of gasses that can be retained under given escape velocity and temperature; each colored band represents a different set of gasses that can only be reliably retained by planets in or above that band. Cmglee, Wikimedia

So for a planet with a composition similar to Earth and a temperature of, let’s say, 300 K, this leads us to a naïve estimate for the minimum mass of a planet necessary to retain a Nitrogen-dominated atmosphere of 0.03 Earth masses. However, heating of Earth’s upper atmosphere by solar radiation can push the exobase temperature up to to 1500 K, and similar heating should occur for any nitrogen-dominated atmosphere with similar insolation. This gives us a more conservative estimate of 0.32 Earth masses for the minimum mass. There’s not a lot of published literature regarding this question of minimum mass for an earthlike atmosphere, but I’ve found at least one more detailed model⁵³ predicting a critical value of 0.07 Earth masses for a nitrogen atmosphere to last over 4.5 billion years, so my simple model is probably missing some important factors regarding the structure of the atmosphere.

It’s a rough, simplified model, but it does generally match what we observe in our own solar system: massive, cold giant planets in the outer system with thick hydrogen atmospheres; Earth-mass planets like Earth and Venus or smaller but colder bodies like Titan with little hydrogen but thick atmospheres of heavier gasses; sub-Earths and dwarf planets like Mars and Pluto with thin atmospheres; and small dwarf planets and minor bodies with no more than trace atmospheres.

Atmospheres can also be lost due to non-thermal escape. Massive impacts can toss superheated plumes of gas into space (and may also heat the surface, quickening thermal escape). Frequent impacts during formation or the Late Heavy Bombardment may have helped remove the primary atmospheres of all the terrestrial planets and a few late impacts may in particular have contributed to Mars's currently quite thin atmosphere. On the other hand, comets may also deliver large amounts of volatiles to dry planets, potentially more than they cast away, and can substantially alter⁵⁴ the surface chemistry while they're at it.

 

Planets without a strong magnetic field can also lose gasses due to the impacts of solar wind particles, a process called sputtering, but the importance of this escape mechanism is often vastly overstated; a magnetic field prevents sputtering (caused by charged solar wind particles), but does essentially nothing to stop thermal escape (caused by light, which is unaffected by magnetic fields, so it doesn't stop UV or gamma radiation either), and there are few situations where the former could causes significant losses and the latter wouldn't (perhaps a planet orbiting a pulsar or a moon in the radiation belts of a gas giant). Besides which, even if a planet lacks an intrinsic magnetic field produced by the interior, an atmosphere can create its own induced magnetic field through interaction with solar wind, as is the case for Venus. This may even be preferable; because intrinsic magnetic fields direct some solar wind particles towards the poles, a weak intrinsic field may actually increase⁵⁵ atmospheric losses. 

An important point to bear in mind is that most of the processes we've discussed are quite rapid compared to the billions of years a planet may remain geologically active or habitable, so rather than gradually adding or removing gasses they tend to quickly move towards equilibrium, where gains from atmospheric sources are matched by losses to atmospheric sinks (as a gas builds up to higher partial pressure this will usually quicken sequestration and escape, so this doesn't require any wild coincidences). On early Earth, for example, oxygen sequestration far outpaced production, so oxygen was virtually absent from the atmosphere for billions of years; but production rose and sequestration declined until the former surpassed the latter about 2.4 billion years ago, at which point oxygen rapidly became a major component of the atmosphere. Levels continued to fluctuate thereafter, but mostly due to shifts in gain and loss rates, shifting the equilibrium.

Rough diagram of the likely most common atmospheric gasses based on planet mass (which controls escape velocity) and solar irradiation (which controls surface temperature) due to various escape mechanisms; the exact boundaries here are inexact because they can vary depending on numerous minor factors. Lichtenberg et al. 2022.

The balance of all these potential sources and sinks and the typical chemistry of rocky planets gives us some sense of which types of atmospheres we should expect to be most common. But there's still plenty of room for variation, and a fair bit of uncertainty due to how complex the interactions of different mechanisms can become. Water, for example, appears to have a high-enough molar mass and inert-enough chemistry to be retained in the atmosphere any Earthlike planet, but photolysis in the upper atmosphere can break it into hydrogen, which easily escapes, and oxygen, which will likely sequester on the surface. However, a nitrogen-rich atmosphere prevents this by forming a cold trap, a layer of the atmosphere cold enough to cause water to condense and rain back down to the surface, removing it from the atmosphere for the moment but preventing permanent escape to space. Recognizing these processes (not to mention something more complex like the carbonate-silicate cycle) requires having a fairly detailed model of Earth's surface conditions, which we just don't have for many of the more speculative cases we'll be discussing today.

This is especially relevant to the common assumption that a bigger planet with higher gravity must always have a thicker atmosphere. There is some truth to this; in the extreme cases, a sufficiently small planet will lack the gravity to retain any more than a trace atmosphere and a sufficiently massive planet will accrete enough hydrogen as it forms to become a gas giant. Even closer to Earth's mass, larger planets should generally have hotter interiors and more sustained outgassing from volcanic activity (though that activity could also cause more sequestration of certain gasses) and atmospheric escape of all kinds slows for greater escape velocity, so we should expect some correlation (higher gravity also holds the atmosphere closer to the surface, creating a higher surface pressure for a given atmospheric mass per surface area). But different planet chemistries and histories can create vastly different sources and sinks that can create much greater variance in the ultimate atmospheric mass and composition than the influence of a small difference in mass. Within our own solar system, Venus and Titan both have greater surface pressures than the more massive Earth. Even if we restricted ourselves to more Earthlike temperatures and atmospheres, I wouldn't be especially surprised to encounter a world half Earth's mass with a greater surface pressure or one twice Earth's mass with less.

Presuming you do manage to settle on a particular atmospheric composition, a few final notes: First, for a planet with a given surface pressure, pressure will fall more quickly with altitude for planets with higher surface gravity and average molar mass. More precisely:

 

 

p = pressure (bar)

p₀ = pressure at 0 altitude (bar)

e ≈ 2.71

g = surface gravity (Earth gs)

h = altitude (meters)

m = gas average molar mass (g/mol)

For convenience I'll use the unit of bar for pressure throughout this post, which is about the average sea level pressure on Earth but slightly less because it comes out to more convenient SI units (100 kPa rather than 101.3 kPa) and so is commonly used by atmospheric scientists (but the above formula should work with any pressure unit).

There is no sharp boundary for the top of an atmosphere; the density of gasses continuously drops until it reaches that of the interplanetary medium. Rough boundaries can be marked where the chemistry and behavior of that thin medium is dominated by the planet rather than the star, but this boundary lies far beyond the point where life could exist or orbiting objects would stop experiencing significant drag. By convention the boundary of space is often set at the “Karman line” at 100 km altitude above Earth, where the pressure is roughly 0.000001 bar, though even at 2-3 times this altitude there is still enough thin gas to cause satellite orbits to decays within a few days or weeks. The exobase where Jeans escape occurs is at around 500 to 1,000 km.

Atmospheres can warm a planet due to the greenhouse effect, but thick atmospheres can reflect away most sunlight before it reaches the surface. Very broadly, an atmosphere with Earth’s surface pressure should lead to higher surface temperatures than one with a pressure 100 times higher or lower, but there are plenty of exceptions, especially given that very thick atmospheres are often composed mostly of greenhouse gasses.

Hydrogen

By far the most common gas in the universe, and we expect that pretty much all large planets should initially form with a hydrogen/helium-dominated atmosphere. But it's also the lightest gas by molar mass and so escapes pretty easily. Generally speaking, we expect most bodies above 2 Earth masses should have thick hydrogen atmospheres and most smaller ones should lack it, but there's plenty of grey area: even gas giants could lose most of their atmospheres through impacts or intense solar heating, leaving their bare cores as cthonian planets of 10 Earth masses or more, and planets below Earth's mass could keep their hydrogen atmospheres to form gas dwarfs if sufficiently cold (below ~100 K).

Within a gas giant, most of the hydrogen does not exist as a gas. Using Jupiter as a model, the visible surface is 50-kilometer-thick region of clouds, blocking most light from reaching the interior. Below that the pressure and temperature gradually increases, reaching levels so high that there’s no sharp distinction between gas and liquid; the hydrogen exists as a supercritical fluid, with a mix of gas-like and liquid-like properties and becoming more liquid-like with increasing depth and pressure. Around 15,000 kilometers down—1/5 of the radius—the hydrogen is expected to behave as a metal, though still not a solid. It's still unclear whether there is a solid core of rock, ice, and metal under all this, or if this material has all dissolved into the metallic hydrogen.

Kelvinsong; Wikimedia

Ice giants have outer layers of hydrogen gas and supercritical fluid, but unlike gas giants their interiors probably lack metallic hydrogen and are instead dominated by supercritical phases of the other volatiles that make up the bulk of their mass.

Terrestrial planets like Earth and Venus likely form with hydrogen atmospheres of 10s to 100s of bar. On Earth, this was probably completely lost within a few 100 million years, but planets just a bit larger or colder could plausibly retain some hydrogen; exactly how much will depend on a variety of processes in planet formation and later evolution, so essentially anything between a thin remnant atmosphere and one approaching that of a gas giant is conceivable. Even if the primary hydrogen-dominated atmosphere is lost, a more reducing internal chemistry may cause volcanoes to outgas hydrogen, maintaining a hydrogen-rich atmosphere even for smaller planets⁵⁶. In any case, hydrogen can act as a greenhouse gas in the presence of nitrogen or other gasses, and this may have helped⁵⁷ warm the early Earth. But it is also a strongly reducing, meaning it cannot exist alongside oxygen, which may pose issues for the development of complex life.

If thick enough to obscure the solid surface, then the outward appearance⁵⁸ of an H₂/He atmosphere will depend on the clouds and hazes that form at the top of the atmosphere, which in turn depends mostly on temperature but also on composition and surface gravity. There are many possible variations, but here's a quick overview of the general trends⁵⁹ that we should expect:

 

Image of Neptune. NASA / JPL / Voyager-ISS / Justin Cowart

The coldest atmospheres, below 100 K, will have low-lying methane clouds, contributing to a blue color, though this is also largely due to Reyleigh scattering (the same effect that makes Earth's sky blue).  Albedo is around 0.3.

Image of Jupiter. NASA, ESA, A. Simon (Goddard SpaceFlight Center) and M.H. Wong (University of California, Berkeley)

At around 100 to 150 K, ammonia clouds appear with traces of carbon and sulfur compounds that result in the yellow-brown color. Lower-mass giants like Saturn may have a high haze that gives them a homogeneous appearance, but higher gravity can reduce this haze and show cloud bands colored red, orange, and gold due to production of unstable trace gasses by sunlight, as for Jupiter. Albedo is around 0.4.

Concept of HD 189733b. NASA, ESA, M. Kornmesser

At higher temperatures of around 150 to 350 K, water clouds like Earth may appear that are predominantly white with an albedo as high as 0.8. At higher temperatures, these clouds may disappear and the color may return again to blue due to Reyleigh scattering. However, recent research⁶⁰ suggests that at 250 to 700 K, a sulfur haze may form above any clouds, turning the planet orange with an albedo of 0.6.

 

Illustration of HD 149026b. NASA/JPL-Caltech/T. Pyle (SSC)

Above 600 K, compounds of silicon, sulfur, alkali metals (lithium, sodium, potassium), and halides (fluorine, chlorine) may appear, tinting the atmosphere brown or green. Above 900 K, a very dark haze of sodium and potassium forms, making the planet black or dark brown with a very low albedo (~0.03), perhaps with a reddish glow due to the incandescence of the hotter lower atmosphere.

Appearance of the day side of hot giants depending on temperature and cloud composition. A real planet would have a mix of these clouds, with those in the lower rows tending to form highest and so be more prominent at lower temperatures. NASA/JPL-Caltech/University of Arizona

At even higher temperatures⁶¹, a variety of metal sulfides, oxides, and silicates appear, coloring the planet grey, brown, or red, with a moderate albedo (~0.1-0.3), though the intense light on these planets will tend to make them appear fairly bright regardless. The intense heating will also cause strong winds between the day and night sides, creating gaps in the haze and revealing a blue lower atmosphere. The unlit nightside will glow a dim red. A blue halo may also appear of lighter gasses escaping to space, and in extreme cases even a comet-like tail.

 

(You can also check out this more detailed breakdown⁶² made by the folks over at Orion's Arm, which contains some more speculative options.) 

Helium

All hydrogen-dominated atmospheres will contain some helium as well, though in gas giant atmospheres the helium may tend to rain out⁶³ into the metallic hydrogen layer, leaving the upper atmosphere relatively poor in helium compared to the typical 3:1 mix.

Under the right conditions⁶⁴, a Neptune-like gas giant in a close orbit of its star may lose most of its initial hydrogen atmosphere but retain its helium. The resulting planet will likely have a whitish color and high albedo.

Concept of GJ 436b. NASA/JPL-Caltech

It's also conceivable that a planet of just the right mass to retain helium but not hydrogen might lose its primary hydrogen-helium atmosphere initially and then gain some helium later as a byproduct of radioisotope decay, though this will probably be only a minor component of the resulting atmosphere unless it is very thin.

 

Alternatively, a white dwarf star may lose most of its mass⁶⁵ in a close encounter with a neutron star or be broken apart in some other way, leaving a small remnant with a helium- or carbon-dominated atmosphere.

As a quick aside, a "hot Neptune" too small or hot to retain helium will likely end up⁶⁶ with an atmosphere of either water, hydrocarbons, or one of the two mixed with CO or CO₂, depending on the C/O ratio and temperature. In principle, a very carbon-poor planet with complete hydrogen loss could be left with mostly oxygen, though that may depend on more details of the planet's chemistry than was modeled in that source.

Nitrogen

The main component of Earth’s atmosphere (78% by volume) as well as that of Titan (95%) and a major component of Venus’s atmosphere (3.5%). A nitrogen-rich atmosphere has also been proposed⁶⁷ for early Mars, though it's one of several competing models. That nitrogen is so common in the solar system across rather different atmospheres likely indicates it's common elsewhere, likely initially delivered to forming planets by ammonia (NH₃)-rich comets and then outgassing later. Plate tectonics or other processes that oxidize the upper mantle may encourage⁶⁸ this outgassing, and indeed Earth's atmospheric nitrogen appears to have increased⁶⁹ over time as its geology and chemistry evolved. But given that Venus has 3 times as much atmospheric nitrogen as Earth, the ultimate level may vary greatly even between similar planets. 

N₂ is relatively inert compared to most other atmospheric gasses—the two nitrogen atoms are joined by a strong triple bond, preventing most chemical reactions—and while it does appear⁷⁰ to cycle into the interior over long periods, it isn’t often incorporated into surface minerals like oxygen, CO₂, and water often are. This also means it can exist in stable mixes with many other gasses.

Image of Earth. NASA

Though atmospheric nitrogen doesn’t interact directly with most life, it has 2 important roles in maintaining Earth’s habitability: First, it creates a cold trap in the atmosphere that causes rising water vapor to condense and rain back down, keeping it from the upper atmosphere where it might escape; Second, nitrogen gas can be “fixed” by lightning or microbes into vital nutrients like ammonium (NH₄⁺) and nitrate (NO₃^-). It’s hard to say if this makes atmospheric nitrogen necessary for life, but at any rate it certainly appears helpful. In turn, oceanic life appears to encourage⁷¹ higher atmospheric nitrogen.

Though Earth is blue primarily due to its oceans, nitrogen contributes as well. Any “colorless” gas will tend to appear blue in thick atmospheres, due to Rayleigh scattering. Even icy or desert worlds may appear blue⁷² if they have thick nitrogen atmospheres.

Oxygen

A major component of Earth’s atmosphere (21%) but absent from other atmospheres in the solar system save for the very thin, transient atmospheres of some icy moons (due to photolysis of the surface ice). Free oxygen’s (O₂) rarity is due to its highly reactive nature, and on Earth it’s only sustained by the action of photosynthetic life. But though oxygenic photosynthesis evolved around 3 billion years ago, consistently high oxygen levels have only existed⁷³ for the last 6-800 million years. Before then, excess oxygen was mostly sequestered by reactions with surface materials to create oxide rocks and, save for a brief period around 2.3 to 2 billion years ago, concentration was below 1/100 of current values. How oxygenic life eventually came to overcome these oxygen sinks is a complex question, possibly relating to gradual geochemical changes in the surface and the growth of the continents⁷⁴, but it's a subject we'll have to leave for another time.

However, there are a few conceivable pathways by which large amounts of free oxygen could be produced without life, predominantly by photolysis; breakdown of compounds by light.

First off, I mentioned that "hot Neptunes" might form oxygen-rich atmospheres if they lose enough hydrogen and I'll mention later that a planet heated to the point of melting its surface might release some oxygen, but I'm not confident that these predictions would stand up to a deeper analysis of these planets' chemistry nor that these atmospheres could survive if the planets cooled to an Earthlike temperature.

UV radiation can photolyze water (H₂O) into H₂ and O₂. The H₂ escapes to space much more easily, leaving excess O₂ behind. The cold trap formed by nitrogen (or a similar gas like argon) limits the rate at which water reaches the upper atmosphere, where it can be exposed to UV and photolyzed. A warm-enough atmosphere could allow significant levels of water to pass the cold trap; this is called a moist greenhouse, as the large amounts of atmospheric water will cause a strong greenhouse effect, warming the surface to over 340 K and causing rates of water loss great enough to dry out the surface in a geologically short period of time. This may occur for a brief period as planets cool after formation, but the molten early crust will typically absorb all of the produced oxygen. But if a planet is fairly dry⁷⁵ (with less than about a third the water as Earth), the crust may solidify faster, leaving significant oxygen that could persist for billions of years if the planet is relatively inactive and doesn't produce much more crust that would sequester it.

At the opposite end of the scale, a waterworld with global oceans over 50 km deep may suppress the formation of new crust, similarly leaving no oxygen sinks, such that even the low rates of photolytic oxygen production with a cold trap would eventually accumulate to high levels over billions of years.

Alternatively, an otherwise Earthlike world without any nitrogen would form a water-dominated atmosphere without a cold trap. Oxygen would form by photolysis until it formed a cold trap, which should occur⁷⁶ at roughly 0.15 bar of oxygen—slightly less if there is some small amount of nitrogen or argon. Some water would be continuously lost, but over 4 billion years this would only amount to about 1/4 of Earth’s current oceans.

But the best prospects for abiotic oxygen may be for planets of red dwarf stars. First off, planets of mid-range red dwarfs⁷⁷ could achieve a moist greenhouse at much lower temperatures, as low as 280 K, and retain oceans for billions of years, allowing for a planet with both habitable temperatures and significant abiotic O₂. Even without a moist greenhouse, the high UV output of a young red dwarf star may photolyze large amounts of water in spite of the cold trap, potentially producing⁷⁸ 100s of bar of O₂, though how much of this would be sequestered hasn't been investigated.

CO₂ can also be split to produce oxygen⁷⁹ around red dwarfs, with or without water present, potentially reaching over 1 bar of O₂, depending on the CO₂ level (~0.1 bar of CO₂ is required for 1 bar of O₂ and 5 bar of CO₂ could give 100 bar of O₂) However, a smaller amount (~0.05-1 bar) of carbon monoxide (CO) is also produced, which may be problematic for human habitation (any native life would presumably adapt to tolerate it).

Several scenarios for production of O₂-rich atmospheres. Meadows et al. 2017

Finally, large amounts of titania (TiO₂) delivered to a planetary surface by meteorites could catalyze⁸⁰ the photolysis of water by lower-energy near-UV light that can more easily penetrate through the atmosphere to reach the surface.

Once oxygen does reach high levels, it will produce an ozone (O₃) layer in the upper atmosphere that can reflect away harmful UV radiation, and it will allow aerobic (O₂-consuming) life to develop into more complex and energy-intensive forms. If complex life does evolve and vegetation becomes a major feature of that surface, the flammability of that vegetation may control⁸¹ O₂ levels thereafter; on Earth, vegetation is difficult to burn below 16% atmospheric oxygen, allowing levels to rise without being consumed in large fires, but far more flammable above 22%, consuming excess oxygen and bringing levels back down (though the greater diversity of vegetation in nature than was used in this study and likely evolution of fire resistance in response to oxygen levels may widen these bounds). Perhaps for this reason, oxygen levels have remained fairly close to 20% (~15-30%) since the appearance of widespread forests 350 million years ago.

Like nitrogen, oxygen should appear blue in thick atmospheres.

Carbon Dioxide

The primary component of Venus’s (96.5%) and Mars’s (95%) atmospheres. On Earth it’s a minor gas (0.04% and rising) but it is the primary gas responsible for the surface temperature, due to the greenhouse effect. Technically water is Earth's primary greenhouse gas, but because water vapor condenses to a liquid so easily, it would be unstable on its own and is in effect controlled by CO₂ levels, amplifying its effect. 

CO₂ should be pretty common as an atmospheric gas, as it should be regularly produced in the interiors of planets that are not heavily reduced and then outgassed by volcanoes. If there is water in the atmosphere, the gasses will mix to produce carbonic acid (H₂CO₃) that will react with surface materials (primarily calcium on Earth) to produce carbonate minerals. Feedbacks in this process control the surface level of CO₂, but given their profound role in habitability, we’ll leave a detailed discussion of them to the next post.

But if there is no water, suitable surface materials to react with, or other process to sequester CO₂, it can accumulate in the atmosphere to high levels, resulting in something like Venus's 90 bar of CO₂, with a strong greenhouse effect producing high surface temperatures (~700 K on Venus). This is expected to be the typical result of a moist greenhouse or runaway greenhouse scenario, where the surface becomes hot enough to force water into the upper atmosphere, where it is then lost to space. This can occur for a planet inside the inner edge of the habitable zone (which we'll discuss in the next post) or even within the inner habitable zone if CO₂ production outruns sequestration and levels rise high enough. But with the weaker solar heating past around 1.36 AU (from a sunlike star), CO₂ alone can never get the surface hot enough⁸², as the levels required for that much greenhouse heating are higher than the levels at which CO₂ clouds form, increasing the planet's albedo and cooling it (likely to the point of freezing over).

When a hot, CO₂-dominated atmosphere does form, what little water that remains may react with volcanic sulfur compounds to produce thick, beige-white clouds of sulfuric acid (H₂SO₄), as we see on Venus. Various other hazes⁸³ of sulfur-based or organic compounds could form for similar planets, likely similarly beige, orange, or brown, and even white water clouds may be possible⁸⁴ for planets with less active volcanism or cooler stars.

Venus in true color; most images you see with clear cloud formations are false-color composites including UV light. NASA

Though it warms the surface, CO₂ also cools the upper atmosphere; Venus actually has a colder upper atmosphere than Earth. Paradoxical though this may seem, the same properties are responsible for both effects: near the surface, CO₂ absorbs heat from the ground and radiates it back down, trapping heat in the lower atmosphere; in the upper atmosphere, CO₂ absorbs heat from the surrounding gasses and efficiently radiates it into space. Because the upper atmosphere is so thin, this cooling has almost no direct impact on surface temperature, but it can slow down thermal escape of atmospheric gasses. In combination with CO₂’s high molecular mass this means that, at a given surface temperature, the minimum mass limit for a body to retain a CO₂-dominated atmosphere should be lower than for an nitrogen-dominated atmosphere.

Carbon Monoxide

The chemically reduced counterpart to CO₂. CO is fairly common cosmically, forming a significant portion of the ice in many comets, but is vanishingly rare on Earth and most other large bodies because of sunlight-aided reactions with water vapor that oxidize it to CO₂. Still, there are a couple scenarios where it might be more stable:

As previously mentioned, for planets of red dwarfs, photolysis in atmospheres with at least 0.1 bar of CO₂ could provide⁷⁹ a steady source of CO, enough to maintain over 0.1 bar even with water present (because the weaker UV light from red dwarfs makes CO and water less prone to react), and larger amounts might form on a dry world.  A larger amount of oxygen should usually form as well, but that could conceivably⁸⁵ be sequestered on the surface.

Similarly, if life produced large amounts of organic carbonyls (a family of organic molecules including formaldehyde (CH₂O)), their photolysis could produce CO as a byproduct, which could accumulate⁸⁶ to high levels for planets of red dwarfs, especially in H₂-rich atmospheres (the carbonyls themselves dissolve easily in water or hydrocarbons and so are unlikely to build up to high levels in the atmosphere).

Alternatively, strongly reducing interior chemistry, like that of a carbon world, may cause volcanoes to outgas CO in place of CO₂, alongside CH₄ or H₂ as we'll discuss shortly. On a carbon world, there may also be no water to react with the CO. This could also occur for a less fully reduced world with a dry surface and volcanism from its deep interior; our moon may have hosted⁸⁷ a thin (~0.01 bar) atmosphere of CO and sulfur during peaks in its volcanic activity.

Finally, as mentioned before, a planet formed by breakup of a white dwarf might be composed of mostly CO, with a CO atmosphere over layers of CO liquid, supercritical fluid, or ice.

Compared to CO₂, CO is not a greenhouse gas and condenses at a much lower temperature, so there may also be a range of conditions where CO₂ and water freeze out of the atmosphere but CO remains.

CO is fairly toxic to complex life on Earth, but there's no strong reason to expect life couldn't adapt elsewhere; some microbes⁸⁶ consume or produce CO in much the same manner as most surface life does with CO₂.

Nitrous Oxide

Nitrous oxide (N₂O) is cosmically rare and rather reactive, but is produced by life during nitrogen use. It's usually promptly converted back to N₂ by metal catalysts or photolysis by UV, but higher biotic N₂O production and a lower UV (so a K- or M-type star) could allow it⁸⁸ to build up to over 0.001 bar, perhaps higher for a planet further out in the habitable zone. So it will probably never be a dominant atmospheric gas, but I thought it worth highlighting because N₂O is a strong greenhouse gas and degrades ozone, so various interesting feedbacks could result, either helping life to maintain ideal temperatures for itself or causing some cascading disaster where a sudden increase or decrease in N₂O production changes the climate.

 

Similar levels of N₂O could also potentially be caused by photochemistry in a more reducing atmosphere (in particular containing CH₄) orbiting a more active star with more flaring activity, as may potentially have happened⁸⁹ for the early Earth.

Water

Some water will exist in the atmosphere of any planet with surface oceans of water like Earth (~0.25% average, locally 0.001-5%). The amount of water in the atmosphere is largely controlled by temperature, and, as water is a greenhouse gas, this leads to an unstable feedback: at low temperatures, water mostly rains down to the surface and other greenhouse gasses like CO₂ are required to keep temperature high enough to prevent the planet freezing over completely; if temperatures get high enough for water to be a major component of the atmosphere, the strong greenhouse effect warms the surface further, evaporating more water, and so on in a runaway that warms the surface well past what we might consider habitable. Earthlike worlds may regularly pass through a stage of steam atmospheres in this runaway state, outgassed from the molten interior during formation, with the water quickly condensing and raining down as the surface cools; but if interior heat remains high and this stage lasts more than a few million years, it could cause significant loss⁹⁰ of the water to space.

However, if a mature, cool planet has no other gasses like N₂ in the atmosphere (or very little of them) and the planet doesn't get too much solar heating, then the low pressure will encourage enough evaporation for a thin but stable water-dominated atmosphere (~0.01 bar⁹¹ for an Earthlike surface temperature, equal to the saturation pressure). Much of this water may escape to space, but as mentioned, enough oxygen may eventually accumulate to form a cold trap, or a waterworld with deep oceans may just have a lot of water to lose, surviving for billions of years⁹² without losing a significant portion of its total mass. As mentioned earlier, a small icy body may also form a water-dominated atmosphere if it migrates inwards, though it would remain very thin, less than 0.005 bar, until the ice surface melts and a runaway begins.

Concept of Kepler-69c. NASA/Ames/JPL-Caltech

Really, though, most planets that form with large amounts of water should also incorporate some ammonia (NH₃), which should then photolyze to N₂ and H₂, the latter of which may or may not escape depending on the escape velocity and temperature. So we should expect⁹³ most temperate waterworlds to have atmospheres dominated by N₂ or H₂, or perhaps occasionally CO₂, CH₄, or O₂.

But what about a planet that does go through a runaway? As mentioned, a world like Earth would lose its oceans fairly quickly and form a dry, CO₂-dominated atmosphere, but a waterworld can sustain a hot steam atmosphere for some time. In some cases it may be possible⁹⁴ for the formation of a thick steam atmosphere (~1-100 bar) to reflect away enough sunlight to (temporarily) stall the runaway and stabilize at a surface temperature of 350-550 K (with the high pressure preventing the ocean surface from evaporating further) Small, low-gravity waterworlds may also stall runaway⁹⁵ by expanding their outer atmospheres as they warm, giving them more surface area to radiate away heat.

In most cases, though, the surface should continue warming past water's critical temperature at 647 K, beyond which there is no longer a distinct liquid ocean; the lower atmosphere and ocean become a supercritical fluid, with a gradual transition from gas-like to liquid-like properties at greater pressures. If the water layer is deep enough, it may transition to odder phases like an ionic fluid where the water dissociates to oxygen and hydrogen ions and superionic ice with a crystal lattice of oxygen through which hydrogen ions travel freely.

Even small amounts of atmospheric water will form clouds, and these clouds can significantly increase the albedo of a world. Earth’s overall albedo is 0.3, even though most of the land and ocean has a lower albedo, due to water clouds. But that albedo could conceivably⁹⁶ vary from 0.25 to 0.5 with fairly minor changes in climate. A thick steam atmosphere could have an albedo as high as 0.8, though at higher temperatures⁹⁷ (>1500 K) fewer clouds will form and this will decline (though, per our discussion of hydrogen atmospheres above, other clouds may become a factor at these higher temperatures).

Hydrocarbons

Methane (CH₄) is a major gas in Titan’s atmosphere (5.7% near the surface), and trace amounts of ethane (C₂H₆) exist there as well. Methane may have existed in significant amounts in Earth's early atmosphere, but was mostly removed once atmospheric oxygen appeared.

Image of Titan. NASA

Methane is commonly outgassed by volcanism under reducing conditions, but as Earth has aged and the crust has oxidized, this has mostly been replaced with CO₂ outgassing. But more sustained reducing chemistry—such as that of a carbon planet—could produce⁹⁸ larger amounts of methane, H₂, and CO for longer periods. Presuming the planet is small enough that the H₂ is mostly lost, for moderate C/O ratios we should generally expect CO or CO₂ to be the dominant gasses, but at very high C/O ratios, methane and other hydrocarbons may replace them. As mentioned earlier, the formation of a silicate crust over a carbide interior may also particularly encourage outgassing of methane and H₂, so it may be possible to see a planet with a broadly Earthlike surface of silicate rocks and water oceans with large amounts of atmospheric methane.

Methane can also be produced in large amounts by life by methanogenesis, either by reaction of existing H₂ and CO₂ or by breakdown of carbohydrates (produced in turn by photosynthesis or a variety of other carbon-fixing processes). Similar abiotic processes⁹⁹ may be able to react CO₂ and acidic water to methane and CO on the surface of some rocks when exposed to UV light. 

A large impact into a planet with a CO₂-rich atmosphere, as may have happened on early Earth, could also⁵⁴ produce a temporary thick atmosphere of H₂ and methane that might persist up to a few 10s of millions of years before these gasses escaped or were sequestered.

There's a whole sequence of hydrocarbons of different carbon chain lengths (following methane (CH₄) and ethane (C₂H₆) are propane (C₃H₈), butane (C₄H₁₀), pentane (C₅H₁₂), etc. as well as variants with more carbon-carbon bonds and fewer hydrogens), with longer-chain compounds tending to have higher melting and evaporation points. Hydrocarbons will tend to bond together into longer chains until they precipitate to the surface as tar. At higher surface temperatures, longer chains can form before this happens, and lighter shorter-chain hydrocarbons are more liable to escape (either directly or by photolysis), so an atmosphere of longer-chain gasses becomes more likely. But hydrocarbons might break down in various ways as well, and atmospheric hydrogen in particular can help hasten this breakdown⁸⁵ and encourage higher methane levels.

Low amounts of methane can act as a strong greenhouse gas, but in an atmosphere with significant CO­₂, a CH₄/CO₂ ratio greater than 0.1 can cause the formation of a haze that will block sunlight lower surface temperature¹⁰⁰. Lacking CO₂, higher levels of methane can also¹⁰¹ react with nitrogen to form tholins, a variety of unstable compounds that form the orange-red haze of Titan. If the methane is produced by either biotic or abiotic surface reactions that depend on sunlight or are slowed at lower temperatures, this could create a negative feedback that limits methane to relatively low levels.

 

Regardless, though a pure methane atmosphere would appear cyan, formation of some amount of haze is likely to tint it yellow or brown. Titan's albedo of around 0.2 may be typical, but it could probably vary greatly depending on the specifics.

Halogens

Fluorine (F) and Chlorine (Cl) can both exist as gasses at Earthlike temperatures, but are somewhat rare and tend to react with surface materials to form stable minerals—though, as mentioned, these will break down at high temperatures. But were we to entertain the idea of seas containing these elements, as we'll discuss shortly, we might imagine that life could produce F₂ or Cl₂ gas in a similar process to production of O₂ on Earth. Alternatively, if a world had extremely salty seas, a photosynthetic pathway might emerge to produce Cl₂ from NaCl. Either gas would probably be more prone to sequestration than oxygen, so such biological production would probably have to be quite vigorous to build much up. Given more carbon-rich conditions, various halocarbons like CF₄ or CH₃Cl could also appear.

Even small amounts of either would tint the sky yellowish-brown. This may make production by photosynthesis self-limiting, as too much halogen production might block sunlight.

Sulfur

Sulfur is commonly outgassed as SO₂ or H₂S, but tends to ultimately deposit in solid or liquid forms. Small amounts of sulfur can form fairly opaque hazes, though; I've already mentioned the likely sulfur hazes (mostly S₈) of temperate H₂ atmospheres, and very high rates of SO₂ outgassing could form similar hazes¹⁰² in N₂ or CO₂ atmospheres. But water vapor will react with SO₂ to produce sulfuric acid (H₂SO₄), which will rain to the surface, preventing such hazes¹⁰³  on any but the driest rocky planets. On Venus⁸⁴, sulfuric acid forms and rains downwards, but evaporates in the hot lower atmosphere before reaching the surface, and so remains in the atmosphere and forms the thick layers of beige clouds, with an albedo of 0.7.

But at even higher temperatures, surpassing 800 K, water may be completely lost to escape or sequestration into the interior (made easier as the hotter surface encourages more melt in the mantle) and sulfide minerals on the surface may dissolve into a thick, CO₂-rich atmosphere, making SO₂ and other sulfur gasses more stable (as the usual pathways to deposition disappear). This is especially true for planets with highly oxidized interiors⁹⁸ that outgas more SO₂. Sufficiently low gravity and high temperature may then cause the CO₂ to escape, leaving heavier SO₂ as the primary gas. A similar scenario may perhaps also leave H₂S as the primary gas for more reduced planets. But these scenarios have not received much detailed study, so I'm not confident that all possible sulfur sinks have been accounted for.

Rock

Concept of KIC 12557548. NASA/JPL-Caltech

At temperatures above 1000 K, parts of the rocky crust may begin to melt and then eventually evaporate, introducing various elements we don't usually think of as volatiles into the atmosphere.

First off, as temperature approaches 1000 K, the crust will thin and some surface materials may begin to melt. Excluding giants that can retain hydrogen or helium, most atmospheres this hot are likely to be dominated by some combination of CO₂, water, N₂, SO₂, H₂S, and hydrocarbons, depending on the sources and sinks present. Presuming the planet is in close orbit of its star (though the heat from a recent impact could also form most of the atmospheres we'll discuss), intense solar radiation may make photolytic O₂ and CO more common. Conversely, a planet with a high C/O ratio may lack O₂ and CO₂ and form clouds of graphite¹⁰⁴, which would then snow down on the surface and form a solid layer.

 

Composition of the atmosphere outgassed from a rocky planet with a surface temperature of 800 K, depending on the internal chemistry (more oxidized to the right). No losses or photolysis are accounted for here; presuming that at least H₂ and H₂O are lost would make the other gasses proportionally more common. Liggins et al. 2022.

Past 1500 K, the surface will melt more completely and atmospheric escape will become significant for most of the gasses we've discussed. Oxygen—both as O₂ and smaller amounts of monoatomic O—may remain common as it is released from the breakdown of melting oxide minerals. Sodium (Na) and potassium (K) will be the first metals to enter the atmosphere at around this temperature. Fluorine (F) and chlorine (Cl) will also enter the atmosphere as their most common minerals break down; if large amounts of water are still present, significant amounts of HF and HCL may form¹⁰⁵. Clouds of sodium and potassium salts may form and then rain back down to the molten surface.

 

If all lighter gasses escape, chlorine and sulfur may remain as the dominant volatiles, with some continuing input of oxygen; what sort of atmospheric mixes may result hasn't received much study. But if all preexisting volatiles completely escapes, the lava ocean will outgas a thin, sodium-dominated atmosphere.

 

Composition of an atmosphere produced above a silicate magma ocean with no preexisting atmosphere, depending on surface temperature. Lammer et al. 2022

At even higher temperatures, silicates begin to break down and enter the atmosphere. Past 2000 K, silicon monoxide (SiO) becomes a major gas, accompanied by small amounts of magnesium (Mg), iron (Fe), and various metal oxiides. These may reform silicate minerals¹⁰⁶ in the cooler upper atmosphere, forming black or grey clouds with very low albedos, though they may also be glowing dull red at these high temperatures. As temperatures increase, the atmosphere becomes thicker again, passing 0.1 bar at around 3000 K, and titanium (Ti), calcium (Ca), and aluminum (Al) oxide clouds may become more prominent. These planets are likely to be tidal-locked, with the sun-facing side much hotter than the nightside, with corresponding variations in atmospheric pressure, causing continuous strong winds¹⁰⁷ from dayside to nightside.

 

But these materials may also escape to space at such high temperatures. In the most extreme case, a planet may develop a comet-like tail of escaping rock vapor.

The atmospheric composition may thus shift as different elements are gradually lost to space completely, the planet effectively evaporating away over time. Magnesium in particular may become dominant¹⁰⁶ as sodium, iron, and silicon are lost.

Gasses produced by a lava ocean at 2200 K with a composition resembling Earth's mantle (top) or continental crust (bottom) as larger portions of the whole are lost. Schaefer and Fegley 2009

Others

There are a huge number possible minor atmospheric gasses; Earth's atmosphere alone has about 20 different gasses in the atmosphere at levels of at least 1 part per billion. But most of these have few sources and many potential sinks so are unlikely to ever appear as major components of an atmosphere. I'll just go over a couple other options here to round off this section. Note as well that most of the liquids I'll mention in the next section could also be atmospheric gasses on planets above their boiling point.

Noble gasses like neon (Ne) (and helium, which we've already discussed) are, as you might expect, gasses at most temperatures, but for that reason tend not to mix into the solid materials that form non-giant planets and may be easily lost with the escape of initial hydrogen-rich atmospheres, with little later outgassing to replace them. Argon (Ar), however, is produced by the radioactive decay of potassium, and so can be gradually outgassed from rocky interiors; today it accounts for 1% of Earth's atmosphere. Also, as with helium and CO, there is perhaps some chance that breakup of a large white dwarf could form a body composed mostly of neon, oxygen, and magnesium, with the resulting atmosphere composed of some mix of neon, O₂, and CO.

Ammonia (NH₃) and hydrogen cyanide (HCN) are both fairly common cosmically, but tend to photolyze or oxidize once mixed into planets. We'll discuss both in more detail in the next section, but in short, neither are likely to be major atmospheric gasses, perhaps building up to 0.001 bar under ideal circumstances (for ammonia¹⁰⁸, an H₂-dominated atmosphere with abundant nitrogen, low UV, and biotic ammonia production; for HCN¹⁰⁹, a very high C/O ratio and some nitrogen). But even at such low levels, these and other gasses (like the aforementioned carbonyls) may help form a variety of prebiotic molecules that later assemble into life.

Oceans

Liquids necessarily exist in an intermediate range of temperature and pressure between solid, gas, and supercritical states. A stable body of liquid on a planet's surface requires some amount of pressure from an atmosphere, hence why I've put oceans last. But if no atmosphere exists, the liquid will create its own by evaporating up to the vapor pressure, though if this gas then escapes to space, continued evaporation of the ocean can lead to its total loss to space. Preventing such rapid escape requires a planet of some minimum mass, depending to some extent on the liquid and the planet's temperature, which is generally high enough that we'd expect internal pressures of that planet to compress basically any material to a solid form. So, aside from perhaps very young, molten bodies, we shouldn't expect to find liquid planets with no solid (or at least supercritical) core.

 

Generalized phase diagram, showing boundaries between the common phases. Modified from Matthieumarechal, Wikimedia

The range of temperatures and pressures required for stable liquids varies greatly, but for our purposes we can generally summarize the extremes with two key points: the triple point, which represents the minimum temperature and pressure at which the liquid can exist (usually; a few materials like water can remain liquid at temperatures below their triple point, but only slightly except at very high pressures); and the critical point, which represents the highest temperature at which liquid can exist and the minimum pressure to remain liquid at that temperature.

 

Past the critical temperature, supercritical fluids can behave similarly to liquids at high pressures (though in most cases the pressure really has to be enormous), but an "ocean" of supercritical fluid would lack a distinct surface, instead transitioning gradually into the atmosphere—as discussed a couple times in the previous section. A planet could also conceivably have deep oceans with a liquid surface that transitions to a supercritical fluid at great depth, but then of course requires that at least the surface be below the critical temperature to form a distinct ocean surface, which I'll presume is what we want in this section.

 

Based on simple assumptions of surface temperature, regions of stability for oceans of different compounds in orbits of different stars. Ballesteros et al. 2019

 

For your convenience, here are these values for most of the materials discussed here, as well as I could determine, as well as the phase-change temperatures at sea level pressure on Earth (I left spaces blank where no good information is available—you can usually assume the triple point is pretty close to the 1-atm melting temperature; for simplicity I rounded molar mass to the nearest g/mol for the most common isotopes rather than averaging for Earth's isotope mix as is usually done; several hydrocarbons and HCONH₂ have inexact melting/boiling points by their nature; He, CO₂, and C sublimate at 1 atm).

Material	Molar mass (g/mol)	Triple Point		Transitions at 1 atm (K)		Critical Point
		Kelvin	bar	melting	boiling	Kelvin	bar
He	4	2.18	0.052	4.22	-	5.20	2.27
H2	2	13.80	0.070	13.99	20.28	32.94	12.86
Ne	20	24.56	0.435	24.56	27.10	44.49	27.69
F2	38	53.48	0.0025	53.48	85.03	144.4	51.72
O2	32	54.36	0.0015	54.36	90.19	154.6	50.43
N2	28	63.15	0.125	63.15	77.36	126.2	33.90
CO	28	68.10	0.154	68.13	81.6	133.2	34.98
Ar	40	83.81	0.689	83.81	87.30	150.7	48.63
C3H8	44	85.47	10-9	85.5	~231	369.5	42.49
SiH4	32	88.48	0.0002	88.1	161.2	269.2	48.45
CF4	88	89.4	0.001	89.5	145.3	227.5	37.45
C2H6	30	89.89	0.00001	90.4	184.6	305.3	48.72
CH4	16	90.68	0.117	90.69	111.6	190.6	45.99
Kr	84	115.8	0.735	115.8	119.9	209.5	55.25
OCS	60	134.3		134.3	223.0	378.8	63.49
C4H10	58	134.6	7*10-6	~136	~273	425.1	37.96
PH3	34	139.4		140.3	185.5	324.5	65.37
C5H12	72	143.46	7*10-7	~143	~309	469.8	33.60
C2H6O	46	150	4*10-9	159.0	351.4	514	63
HCl	36	159.0	0.139	158.9	188.1	324.7	82.56
CS2	76	161.1		161.5	319.4	552	79
Xe	131	161.4	0.818	161.4	165.1	289.7	58.42
Cl2	70	172.1	0.014	171.6	239.1	416.9	79.91
CH3Cl	50	175.4	0.0087	175.8	249.3	416	67.14
CH4O	32	175.5	0.0019	175.6	337.8	513	79.5
CH2O	30			181	254
N2O	44	182.3	0.879	182.3	184.7	309.5	72.40
H2S	34	187.6	0.233	187.7	213.6	373.3	89.7
HF	20	189.8		189.6	292.6	461	65
NH3	17	195.4	0.061	195.4	239.8	405.5	112.8
SO2	64	197.7	0.017	201	263	430.8	78.84
CO2	44	216.6	0.517	194.7	-	304.2	73.80
HNO3	63			231	356	648.5	80.58
Fe(CO)5	196			252.2	376
HCN	27	259.9		259.9	299	456.9	53.20
N2O3	76			261.9	294.8	630.5	66.75
NO2	46			263.8	294.3	431.4	10.13
H2O2	24			272.7	423.3	728	220
H2O	18	273.2	0.0061	273.2	373.2	647.1	220.6
N2H4	32	274.6		275	387	653	147
HCONH2	45	275.6		~275	483
HC­3N	51			278	315.6
H2SO4	98			283.5	610	927	460
H3PO4	98			315.5
K	39	336.35		336.7	1031	2223	160
Na	23			370.9	1156	2573	350
S8	256	388.3	0.00003	388.4	717.8	1314	207
Mg	24	922		923	1363	4100
NaCl	58	1074	0.30	1074	1738	3900	260
FeS2	120			1180
Fe	56			1811	3134	8500
SiO	44			1975	2150
SiO2	60			1986	3220
TiO2	80			2116	3245
Al2O3	102			2345	3250
CaO	56			2886	3120
MgO	30			3125	3870
C	12	4500	101	3915	-

 

Most simple liquids are colorless, but I'll note some exceptions, and they could conceivably be colored by any number of dissolved impurities.

Water

Of course. There’s some debate about exactly how Earth received all its water—in particular whether it was part of the original material that formed the planet or it was delivered later by comets—but however it arrived, some amount of water seems to have made it into every planet and major moon in the solar system, so it doesn’t appear hard to come by. Earth’s water regularly cycles in and out of the interior, such that may be several more ocean’s worth of water stored in the mantle (don't picture giant aquifers; it all exists either mixed into magma or as individual molecules within the crystal structures of certain minerals). Thus, we could probably afford to entirely lose the oceans a couple times over before the planet became completely dry.

Recent research¹¹⁰ indicates that (at least in red dwarf systems) most planets of Earthlike mass are probably either relatively dry like Earth, which is under 0.05% water by mass even including mantle water, or very wet, with a roughly 50% water, and there are few—but not no—planets in between. More recent research¹¹¹ has suggested that many exoplanets identified as small gas giants may be hydrogen-ocean or hycean worlds, with a deep water ocean below a thick H/He atmosphere.

Within the "dry" group, feedbacks between surface oceans and the mantle should tend¹¹² to prevent the surface from being completely inundated while less than 0.2% of the planet’s mass is water, and also tend¹¹³ to reduce the size of these oceans as the mantle ages and cools; Earth 3 billion years ago may have had twice the amount of water in its oceans, and given another 3 billion years the oceans may drop to 1/4 of their current volume were they not likely to boil away first due to the warming sun. So we can mostly expect water oceans to either be partial and (relatively) shallow or global and very deep.

 

Once a global ocean¹¹⁴ gets deep enough—around 150 km deep for an Earth-mass planet with a temperate surface—the pressure at the ocean’s base will be so intense as to force water at the bottom into unusual, dense phases of ice which remain solid to high temperatures. Initially this ice layer is only a few kilometers thick, and heat from the interior can get the base of the ice hot enough to melt again and form a secondary liquid ocean below it. But as the ocean grows deeper, the ice layer thickens and the lower ocean thins. Past around 230 km, the ice layer grows to over 50 km thick and liquid water below it exists only intermittently in a thin layer.

Varieties of waterworld ocean structures, with increasing total depth to the right (depth not to scale). Noack et al. 2016

A world with under half Earth's surface gravity and a surface temperature of 400 K could get¹¹⁵ liquid oceans over 1500 km deep, but such a hot surface would require a thick atmosphere (~10 bar) to stop it boiling—or we could let it boil to produce a thick steam atmosphere, but that could lead into the runaway greenhouse scenario we discussed earlier. An even hotter surface could also cause an even deeper layer of supercritical water to form under the liquid ocean.

Possible internal structures for a planet 8 times Earth's mass composed of 70% water, depending on the pressure and temperature at the surface or top of atmosphere. Nixon and Madhusudhan 2021

On the other end of the scale, dry, cold worlds below water's usual melting point could have small bodies of mineral-rich brines. In the most extreme case¹¹⁶, a lithium-ammonia-rich brine could remain liquid to as little as 90 K.

Open water has a very low albedo of 0.06, but of course water oceans are likely to be accompanied by ice and clouds with much higher albedos. Liquid water is actually blue on its own independent of the color of the atmosphere, but various minor impurities could conceivably alter its color—green being common on some areas of Earth due to the presence of plankton, but just as alien vegetation could be many different colors, alien microbes could color their seas many hues. Earth's oceans may have been tinted several other colors in the past: 

• Earth's early, oxygen-poor oceans may have contained¹¹⁷ significant amounts of ferrous-ferric hydroxy salts, a.k.a. green rust, potentially tinting them green long before green algae appeared.
• When oxygen was first produced 2.5 billion years ago, it would have converted dissolved iron to the more familiar iron oxide rust, tinting the oceans red for a period until enough oxygen accumulated to remove iron from the oceans.
• Even after oxygen appeared, there may have been an extended period, perhaps up to ~1 billion years ago, when the oceans remained relatively oxygen-poor and sulfur-rich, tinting areas of the ocean¹¹⁸ milky white or turquoise with sulfur and perhaps including black patches of bacterial mats and organic debris welling up from the ocean floor near coastlines. It also would have smelled awful.
• Before around 700 million years ago, the dominant photosynthetic life in the oceans may have been¹¹⁹ red or purple algae, tinting large areas pink.

Hydrocarbons

The only other surface liquid in the current solar system is the hydrocarbon lakes of Titan. Titan has a full “methane cycle” analogous to Earth’s water cycle, with clouds, rain, rivers, and seas. The seas themselves are mainly restricted to the poles and are likely composed¹²⁰ of a mix of 3/4 ethane (C₂H₆), 10% methane (CH₄), 7% propane (C₃H₈), and smaller amounts of butane (C₄H₁₀), hydrogen cyanide (HCN), nitrogen (N₂), and Argon (Ar). Unlike Earth's water, there is far more methane¹²¹ within the atmosphere than in the seas, though large amounts may also exist in the crust¹²² as what we might call "groundmethane", like our groundwater.

These seas can form because Titan is cold enough to lock all its water into the ice crust; a warmer Titan would have water-ammonia oceans instead. But a carbon planet could lack water and have hydrocarbon seas up to higher temperatures. Much as we discussed, the methane and ethane might evaporate but may then bond into larger molecules, forming a more viscous sea of tar. What sort of climate cycles such a world might have has not received much formal research. 

The variety of hydrocarbons and the even broader variety of organic molecules they can form when interacting with the atmosphere and surface may make for a lot of chemical complexity. Rain and snow may consist not just of hydrocarbons but also HCN, cyanoacetylene (HC₃N), and more complex tholins—all of which have various melting temperatures, so mixed rain and snow of different compounds may be the norm. The snow may form¹²³ a thin film on the surface of the oceans, damping waves and slowing evaporation.

Sulfur

There are a number of sulfur compounds that exist in liquid form in small amounts throughout the solar system and could conceivably gather into more stable lakes or oceans under slightly different circumstances.

 

First off, Venus has clouds and rain of sulfuric acid (H₂SO₄) in its upper atmosphere, formed from water and volcanic sulfur compounds. Though the temperature and pressure in the lower atmosphere are strictly within the liquid range for H₂SO₄, it nonetheless tends to dissociate in the heat to water and SO₃, which evaporate before reaching the ground. Were Venus cooler (below around 550-600 K), the H₂SO₄ might instead pool on the surface. It might then react with the surface and deposit as various minerals, but sustained volcanism could perhaps supply enough sulfur to eventually saturate these sinks, eventually forming lakes or oceans of H₂SO₄. Even on temperature worlds, high levels of sulfuric volcanism could introduce some H₂SO₄ into water oceans, and various mixes of water and H₂SO₄ could conceivably exist over a broad temperature range.

Under more reducing or water-poor conditions, atmospheric sulfur compounds might instead¹²⁴ form pure sulfur (mostly S₈), which could remain liquid above around 388 K. Io appears to form temporary lakes of molten sulfur (with frozen surfaces) warmed by volcanic activity. Sulfur has a very high critical temperature of 1318 K, and so might form some of the warmest oceans of any typical volatile before temperatures get high enough to melt the whole crust. At temperatures above ~800 K, sulfide minerals like pyrite (FeS₂) may decompose to produce sulfur, which should remain liquid at pressures above a few bar.

And at colder temperatures, volcanic sulfur dioxide (SO₂) or hydrogen sulfide (H₂S) might themselves form seas, though the latter has a narrow range of liquid temperatures. Again, such liquids might exist in pockets below the surface of Io. At a high C/O ratio, carbon disulfide (CS₂) or carbonyl sulfide (OCS) might be possible, but I've never seen more than a passing reference to the idea in the literature.

Various mixes of these liquids could also form, so there is overall a fairly broad range of sulfur seas possible if enough sulfur can be brought to the surface. The appearance could vary greatly: H₂SO₄ and SO₂ are clear but might be tinted by various dissolved minerals; Molten sulfur would vary between transparent yellow at low temperatures, red between around 430 and 470 K, and black at higher temperatures; CS₂ might appear yellow or red.

Ammonia

Ammonia (NH₃) is fairly common in ice in the outer system, and as mentioned may be the ultimate source for nitrogen atmospheres. However, under UV it tends to photolyze to N₂ and H₂, and getting those gasses back to NH₃ is far more difficult. But UV photolysis should be less of a problem for planets orbiting redder stars or protected by thick atmospheres or surface ice, and at least one recent study¹²⁵ has suggested that the right mix of hydrogen and nitrogen may make ammonia more stable.

 

The next problem is that ammonia and water ices are often mixed together, with water tending to be more common, and there doesn't seem to be any good way to remove the water and leave the ammonia. Ammonia does have a lower freezing temperature than water, but water/ammonia mixes have a lower freezing temperature than either. Were a water-heavy mix of the liquids to be cooled, the water would freeze first, leaving the remaining liquid ammonia-enriched, up to a maximum¹²⁶ of about 33% ammonia at 176 K; any further cooling would then freeze the whole remaining mix. Thus, we are probably more likely to encounter mixed water/ammonia seas than pure ammonia, and such seas are suspected to exist below the ice of some outer moons like Titan.

 

On its own, ammonia is clear, but dissolved alkali metals might tint an ammonia ocean brown.

Carbon Dioxide

CO₂ is not usually thought of as likely to form seas due to its high triple point pressure; a surface pressure of at least 5.18 bar is required for liquid CO₂ to form. If a planet has volcanic CO₂ outgassing which outpaces any sequestration (requiring either a dry surface, low sunlight, or very high rates of volcanism) then this isn't that hard to achieve, as we can see on Venus, but then the greenhouse heating may raise the surface temperature beyond CO₂'s critical point at 304 K.

But for planets with less sunlight¹²⁷ (beyond about 1.5 AU from a sunlike star) such that temperatures remain lower, CO₂ clouds can form as CO₂ levels increase, cooling the planets by raising its albedo and eventually overcoming the greenhouse effect and causing temperatures to drop with further increases in CO₂. Lower temperatures tend to slow sequestration, so the CO₂ should continue to accumulate until the surface is cold enough for it to rain out, forming oceans on the surface. This removes excess CO₂ from the atmosphere, preventing further cooling and stabilizing the climate. Planets near the inner boundary of this region could also oscillate between cool states with CO₂ oceans and warm states where they boil off due to destabilizing climate feedbacks.

Mixed water-CO₂ oceans could also form this way, though if temperature drops below 283 K (not far below CO₂'s critical point), the CO₂ would instead become trapped in clathrates, water ice with trapped gas, which would accumulate on the floor of the water ocean.

I can't say much about how these oceans would appear (liquid CO₂ itself is clear), but given the very thick, cloudy atmospheres formed in this process (around 20 bar), these worlds might be pretty dark.

Nitrogen

Nitrogen (N₂) ice is common on some small bodies of the outer solar; if any of these were larger and had a substantial atmosphere (above 0.13 bar and 63 K), they might conceivably allow for the ice to melt, while other volatiles remain frozen. Pockets of liquid N₂ are believed by some³² to exist below the surface of Triton.

Hydrogen

Hydrogen (H₂)is an obvious candidate, given how common it is as a gas. The main issue is that its critical point is a mere 33 K; even without any solar heating, an Earthlike planet with a hydrogen atmosphere will likely retain a higher surface temperature than that just through retention of geothermal heat, and larger planets more likely to have atmospheric hydrogen will tend to retain even more internal heat. Still, geothermal heating declines with age and it is just about conceivable that there may be old rogue planets out there (orbiting no star) that are both large enough to have formed with a hydrogen-rich atmosphere and small enough to have cooled below its boiling point, allowing hydrogen seas to form.

Hydrogen Cyanide

Another material that's fairly common in the cosmos but often tends to break down once mixed into planets, though Titan has some in its lakes and clouds. It should be reasonably stable under strongly reducing conditions, and can be produced by UV light, lightning, or impacts, especially¹⁰⁹ at high C/O ratios. For such conditions to form large amounts of HCN but not larger amounts of water or hydrocarbons seems unlikely, but might be worth considering nonetheless; HCN is a tad heavier than water and methane, so could conceivably remain if they escaped to space.

Alcohol

Simple alcohols like methanol (CH₃OH) and ethanol (C₂H₅OH) are fairly common in comets and the interstellar medium. They're rarer on planetary bodies in the solar system, though could perhaps have been present on the early Earth, and short-lived methanol seas have been proposed¹²⁸ for early Mars. Though initial delivery of alcohols by comets is likely to be diluted in much larger amounts of water or methane, sunlight-aided oxidation of methane with oxygen or hydrogen peroxide (H₂O₂) could produce more methanol, especially¹²⁹ if helped along by iron or copper catalysts. A methanol/water mix is also possible; in an initially water-heavy mix, the water would freeze out first at low temperatures, and unlike ammonia the remaining liquid would become methanol-dominated—up to¹³⁰ 88% before completely freezing at 157 K.

The main issue is that the same materials that oxidize methane to methanol would also tend to further oxidize methanol to and water. Preventing this likely requires either a very well-timed shift in surface chemistry or geochemical processes that add methane and oxygen and remove water.

Formamide

Formamide (HCONH₂) is a fairly uncommon volatile in the cosmos but easily formed by the reaction of water and HCN, or by lightning or impact events in an atmosphere with a mix of the CHON elements, and likely did form in at least small amounts on the young Earth. As it has a higher boiling point than water (483 K at 1 bar), a pond of mixed water and formamide in a hot, dry environment will tend to lose water until only the formamide remains. But in a wetter environment, the formamide will break down again, and an oxidizing atmosphere will inhibit the formation of cyanide; so formamide no longer forms in large amounts on Earth, but perhaps a dryer world with a reducing atmosphere could form persistent lakes or seas of formamide. Various mixes of formamide with water, HCN, or hydrocarbons could also be possible.

These possibilities are intriguing because liquid formamide provides an excellent environment for the formation of complex organic molecules. Some researchers¹³¹ have even proposed that life on Earth may have begun in isolated formamide ponds and then only later spread into the water oceans.

Halogens

Fluorine (F) and chlorine (Cl) (part of the group of halogen elements) are not terribly common, but they are somewhat concentrated in Earth's crust, forming a variety of minerals, and it is conceivable that they might be even more concentrated on another planet, with volcanic activity thus producing some amount of HF or HCl. Usually we'd expect such conditions to also produce larger amounts of water, but perhaps if the water escaped into space or was locked in the mantle¹³², the halogens that remained in the crust could then produce HF or HCl seas through later volcanism.

 

Initial seas of sulfuric acid might also help release halogens from the crust, forming mixed oceans; perhaps the sulfur could later be preferentially sequestered, but that's wild speculation on my part. Remember as well that on planets heated to over 1000 K, HCl and SO₂ might become the dominant volatiles if all lighter gasses escaped; perhaps later cooling could then allow the HCl to rain back down and form seas (though avoiding deposition of the chlorine in salts may be difficult). A large impact event that temporarily melted the crust might provide¹³³ the ideal circumstances for this intense heating and then cooling.

Under more carbon-rich conditions, these processes might also produce halocarbons (CF₄, CHCl₃), which much like regular hydrocarbons can assemble into larger molecules.

None of these scenarios seem especially likely or have been explored in much depth, but they are tantalizing as HF and HCl are similar to water in many ways but abundant halogens could allow for intriguing new forms of biochemistry, which we'll discuss in a later post.

Lava

Much as we discussed in the atmospheres section, many materials we don't usually think of as forming oceans might do so if the surface gets hot enough. Essentially all substantial planets should pass through a molten stage as they form, and later large impacts could also briefly melt at least part of the surface. How long these temporary lava seas last depends strongly¹³⁴ on how thick of an atmosphere forms from gasses released from the rock as it melts; if the rock is relatively "dry" and the atmosphere remains thin, the surface will cool and solidify within a few thousand years; but if a thick steam or CO₂ atmosphere forms, this could help trap heat and keep the surface molten for 10s of million of years. If a thick steam atmosphere forms and the planet is relatively close to its star (within ~0.8 AU from a sunlike star), the runaway greenhouse heating may keep the surface molten¹³⁶ for as long as outgassing of water from the lava ocean can replace atmospheric losses; potentially billions of years for a body with 10 or more times Earth's water content.

 

Time of survival for a global lava ocean for an Earthlike planet with an albedo of 0.2 orbiting a sunlike star based on orbital distance and water content (1 M_EO being equivalent to Earth's oceans). Hamano et al. 2015

Internal sources of heat from radioisotope decay or tidal heating may make it easier for the surface to melt but are unlikely to keep it molten on their own for long; radioisotope concentrations would need to be absurdly high to produce enough heat (some short-lived isotopes like aluminum-26 might help keep planets molten for longer when they first form but will then near completely decay away within a few million years) and tidal forces strong enough to induce that much heating should also quickly change the planet's orbit or rotation to reduce that heating.

The longest-lived lava oceans will form on planets close enough to their stars to be heated above their boiling point regardless of the presence of an atmosphere. Any such planet will form a rock vapor atmosphere and likely experience atmospheric escape, such that the whole planet will essentially evaporate away given time; this might take¹³⁶ around a billion years for an Earth-mass planet heated to over 2000 K, but could be a good deal longer for more massive planets.

As mentioned, sulfide minerals may decompose at around 800 K, potentially producing molten sulfur. Alkali salts like NaCl will melt at 1000-1500 K and could perhaps pool on the surface if the planet retains a thick enough atmosphere to keep them liquid. The silicates that make up the bulk of rock will mostly melt at 1500-2000 K. As these materials melt, they'll also vaporize and escape to space, leaving the lava more enriched with less volatile materials like calcium and aluminum oxide (CaO and Al₂O₃) which may then solidify again, but even these will melt at ~2200 K. More iron-rich lavas may be possible if the rocky mantle has been mostly removed before the surface melts, but otherwise iron tends to more readily vaporize and escape to space than other metals.

Any planet orbiting its star close enough to be heated to such extremes is likely to be tidal-locked to it. Presuming any preexisting volatile atmosphere has been lost, if the dayside temperature remains below 3500 K then the rock vapor atmosphere will be quite thin and it and the viscous lava ocean will transport heat poorly. For a dayside peak temperature of 2500 K, the nightside could remain¹³⁷ as cold as 50 K. 

Concept of CoRoT-7b. Leger et al. 2011

The result is what we might call a "lava eyeball world": The dayside would be dominated by a circular lava ocean, with a shoreline where the surface temperature drops below its melting point. There would be a fairly broad partially molten region¹³⁸ along the shore, probably with a thin solid crust; perhaps convection currents in the ocean could pull off sections of rock just as icebergs calve off of glaciers into our oceans.

Rock vapor will evaporate off the magma ocean and deposit on the nightside crust, forming a pressure gradient and thus prevailing winds towards the nightside with windspeeds as high as kilometers per second (though that's less dramatic than it sounds in such a thin atmosphere). Metals will crystallize and snow out of the vapor at different temperatures, forming concentric rings of solid metals or metal oxides on the crust around the ocean's shores.

Finally, the nightside will be cold enough that an icecap of water or other volatiles could conceivably form, bizarre as that may sound under the circumstances. Before you ask, air pressure is too low for surface liquid water to exist in the transition zone; the silicate atmosphere freezes out before reaching the nightside, and any more volatile gasses would rapidly escape on reaching the dayside, so in effect the nightside has no atmosphere. But local water aquifers under the ice are a possibility, and so life may be as well.

Above 3500 K, the atmosphere is thick and hot enough to melt the whole surface¹³⁹ of even a tidal-locked planet. Albedo of a molten rock surface may be around 0.1, though alkali and silicate clouds may darken the planet further—not that they'll look dark under such intense light, and at such high temperatures the planet itself will glow red.

Others

In addition to those liquids mentioned, there are a number of other liquids that have been suggested at one point or another as possibly forming lakes or seas, but have received almost no formal study.

 

Carbon monoxide (CO) is a fairly common ice on very cold bodies, and has a similar triple point to nitrogen (0.15 bar and 68 K), so should similarly be a possible liquid on larger cold bodies than we see in the solar system, though may be restricted to more reducing conditions. Perhaps N₂-CO mixes could even occur.

While we're at it, oxygen (O₂) also has a similar but somewhat more permissive triple point (0.0015 bar and 54 K), but of course O₂'s reactivity makes it rare; it could be a tad more stable at low temperatures, but producing large amounts of it might also be more difficult in such conditions (as we wouldn't expect much in the way of vigorous photochemistry or biological activity). Some icy bodies have very thin oxygen atmospheres due to photolysis of surface ice and then hydrogen escape, so perhaps that could condense if it managed to build up to a high-enough pressure.

 

Noble gasses also become liquids at sufficiently low temperatures: helium's (He) critical point of 5.2 K is probably simply too cold for any substantial body to have reached within the current age of the universe, but those of neon (Ne; 45 K) and argon (Ar; 151 K) are more reasonable. As mentioned before, the issue is that these are unlikely to be common on planet surfaces, but there is some argon in Titan's seas, and again we could imagine breakup of an oxygen/neon/magnesium white dwarf forming a body with a neon-rich surface (much as for hydrogen, such a body would probably have to be isolated from solar heating and quite old to get colder than neon's critical point).

 

Metal carbonyls like iron pentacarbonyl (Fe(CO)₅) can form naturally¹⁴⁰ under very reducing and metal-rich conditions and are liquids at similar temperatures and pressures to water and other volatiles, so could perhaps become common under one of the scenarios for formation of a metal-rich surface we discussed earlier. Color would vary, with Fe(CO)₅ tending to be rusty orange.

Hydrogen peroxide (H₂O₂) is usually highly reactive, but could perhaps replace water in very oxidizing conditions. A water-H₂O₂ mix could be an intriguing solvent¹⁴¹ for life in cold, dry conditions like the modern surface of Mars, though pure H₂O₂ might be too oxidizing for life.

Hydrazine (N₂H₄) has similarly been discussed¹²⁹ as an intriguing potential solvent for alien life from a biochemical standpoint, but always with the conclusion that natural bodies of hydrazine are difficult to justify geochemically given how reactive it is.

 

Nitric acid (HNO₃) and various nitrogen oxides (NO₂, N₂O₃, etc.)—which will react with water to form HNO₃—are liquids at decently broad temperature ranges and form in small amounts in a variety of conditions, but are fairly reactive and would likely be stable only in very oxidizing conditions, and even then there doesn't seem to be a good scenario for them to form in the absence of much larger amounts of other volatiles. NO₂ is reddish brown and HNO₃ is clear but would likely be tinted yellow or brown by small amounts of NO₂.

 

Phosphine (PH₃) and phosphoric acid (H₃PO₄) are liquids over fairly broad ranges of temperatures, but rare due to phosphorus's tendency to form stable phosphate materials. But phosphorus bonds more weakly to carbon, so a very high C/O ratio could perhaps make them more likely.

Silane (SiH₄) is liquid under similar conditions to nitrogen, and the two actually mix together pretty well, which may have intriguing implications¹⁴² for the possibility of exotic silicon-based life (though there are still a number of issues we'll discuss at a later time). But silicon has a strong tendency to form stable solids with both oxygen and carbon, and it would be hard to imagine a scenario where both were absent such that large amounts of silane could form.

Alien Skies

Perhaps the most popular and effective way to establish a fictional world as alien and interesting is to have the characters look up, so it would be remiss of me not to address what they might see in our constructed systems. I’ve already discussed the color of the atmosphere; what effect this has on the color of objects seen through the atmosphere depends on exactly why the atmosphere is that color. If the sky is colored due to scattering, that color will be subtracted from light passing through it; the sun appears yellow from Earth’s surface rather than its true white because of the scattering away of blue light. If the sky is colored by particulate matter, this color will be added; any object seen from Mars’s surface will be tinged red (scattered light from one object can also tinge other objects to some extent, if they're far dimmer than the primary light source in the sky).

By way of example, friend of the blog Luke Campbell has done some admirable work modelling the color of skies with varying atmospheric pressure, stellar spectra, and composition; Teacup Ae orbits a K5 star and I'll give it a thicker atmosphere than Earth, so based on these results we can expect a generally paler sky with a slight orange tinge at the horizon that then becomes much more prominent at twilight.

Past that, we can summarize most of what we want to know with two values, the apparent diameter and the apparent magnitude; how big and bright is it in the sky?

The apparent diameter of a spherical body is straightforward trigonometry:

 

 

δ = apparent diameter

r = radius of spherical object (any unit so long as D is the same)

D = distance from observer to center of spherical object

 

For small angles, sin^-1(r/D) will be pretty close to (r/D) anyway (within about 1% error where r/D is less than 1/4), so you can skip the trigonometry in a hurry; so, for example, were the moon 2 times its current distance from the Earth but had 3 times the radius, we would expect it to appear about 3/2 as wide in the sky as it currently does.

 

This incidentally gives you some idea of when eclipses might occur: for, say, a planet's moon to eclipse its star requires that the moon's apparent diameter from the planet's surface be larger than the star's.

Apparent magnitude can be a bit trickier. For a star, an absolute magnitude that is independent of the distance from the observer can be calculated based on luminosity:

 

M = absolute magnitude

L = luminosity (relative to sun)

Note that magnitudes are logarithmic, to match human perception of light; we perceive large changes of luminosity in bright conditions to be equivalent to small changes in dim conditions. This allows us to see details at night without being overwhelmed by excess information in the day, and we should probably expect it to be a trait shared with any organism that has sight as a dominant sense. Note also that brighter objects have lower magnitudes for…historical reasons? I’m honestly not sure. So a decrease of magnitude by 1 corresponds to an increase in luminosity by a factor of ~2.5.

And finally, note that this is a bolometric absolute magnitude, meaning that it accounts for all light across the spectrum. To compare how stars other than the sun would appear to human eyes, we have to apply a bolometric correction factor. Unfortunately there’s no easy, simple formula to estimate this factor, but extensive tables¹⁴³ exist for observed factors for given effective temperatures.

This correction is specific to the spectral range of human vision, of course, but there’s some justification for thinking that an alien organism with a similar natural lifestyle might have a similar visual range, regardless of the star it lives near—more on that when we discuss biology.

Once an absolute magnitude is known—bolometric or visual—the apparent magnitude can be calculated for an observer at a given distance:

 

m = apparent magnitude

M = absolute magnitude

D = distance to observer (parsecs; 1 psc = 3.261 ly = 2.063*10⁵ AU = 3.086*10¹³ km)

For planets (or other similar bodies) the process is similar, starting with a planetary absolute magnitude that indicates the reflection of light by a planet orbiting a given star independent of the planet’s distance from that star or the observer’s distance from the planet—but is not on the same scale as stellar absolute magnitude.

 

H = planetary absolute magnitude

M = star absolute magnitude (4.74 for the sun)

r = planet radius (Earth radii)

p = geometric albedo.

The geometric albedo used here, which represents the light reflected by a planet directly back at the light source, is different from the bond albedo used for the effective temperature calculation before. The two are typically similar but the geometric albedo can be higher or lower than the bond albedo, and for solar system bodies it is usually the former, with airless bodies tending to have the greatest difference. Earth has a bond albedo of 0.3 but a geometric albedo of 0.43.

That in mind, the apparent magnitude of the planet—which is on the same scale as that of stars—can then be approximated based on the relative positions of the star, planet, and observer:

 

m = apparent magnitude

H = planetary absolute magnitude

D_S = distance from star to planet (AU)

D_O = distance from observer to planet (AU)

α = phase angle (degrees); angle between the lines connecting the center of the planet to the star and to the observer.

Modified from Renerpho, Wikimedia

This is a rough approximation, but thanks to the logarithmic scale small errors shouldn’t change the results too much. It also assumes that the bodies are fairly far apart, such that the observer can see most of one hemisphere, and the planet produces no light of its own (if it does, you can use the same magnitude formulas as for stars for this emitted light, and, thanks to the logarithmic scales here, we can assume the light of lower magnitude dominates over the other).

By way of comparison, here are the maximum apparent diameters and magnitudes of several objects as seen from Earth (for Venus, the two maxima are achieved at different times):

Body	Sun	Moon	ISS	Venus	Sirius
Apparent Diameter (°)	0.54	0.57	0.017	0.018	1.6*10-6
Apparent Magnitude	-26.74	-12.90	-5.90	-4.92	-1.47

6.5 apparent magnitude is the approximate limit for detection by human eyes on a clear, moonless night, though if all other stars or sources of light were removed there is no specific limit—the human eye is somewhat sensitive even to individual photons, though we probably can't expect to see extremely dim objects with any detail. The Hubble Space Telescope is sensitive to 31.5 magnitude. There is no such limit for apparent diameter; even a point source of light is visible if it is bright enough. But 0.02° is about the limit to perceive an object as anything other than a point.

So far as I can tell, the largest apparent diameter of any planet viewed from any moon in the solar system is Jupiter as viewed from Metis, at 67° (as mentioned, my apparent magnitude formulas aren’t valid this close, but I’d estimate it to be in the neighborhood of -21 at maximum). Viewed from a flat area on Metis facing Jupiter, the planet would stretch over 1/3 of the distance from horizon to horizon, which means the moon spends 1/6 of its orbit in Jupiter’s shadow. However, for most major moons the planets are surprisingly small in the sky; from Ganymede, Jupiter appears 7.65° in diameter (smaller than the palm of your outstretched hand) and about -16 in magnitude; from Titan, Saturn appears 5.46° in diameter (16.85° including the rings) and -14 in magnitude. They’d certainly make for impressive sights, but not loom across the sky quite as much as sometimes depicted.

But that’s just our system. As a general rule, planets in the habitable zone of stars smaller than the sun will observe their stars to be larger but dimmer in visual light compared to the sun as seen from Earth. In the tightly-packed TRAPPIST-1 system, many of the planets are of similar size to Earth but much closer together. From TRAPPIST-1f—the most likely to be habitable (based purely on its orbit)—the star appears 1.67° in diameter and -20.2 in magnitude (by visual light). The nearby planet TRAPPIST-1e appears 0.48° in diameter at closest approach, almost as large as our own moon. If TRAPPIST-1e were replaced with a Neptune-sized planet, it could actually eclipse the star as seen from TRAPPIST-1f. A larger planet might destabilize that particular system, but at any rate it appears feasible for such interplanetary eclipses to occur in tight systems.

Concept of the system Gliese 581. ESO

The direction to an object in the sky depends on an interplay of distance, inclination, obliquity, latitude, time of day, and time of year that I won’t dig into here. But just as a point of reference, here’s the formula¹⁴⁴ for the maximum angle between the horizon and a satellite—be it a moon, ring system, or whatever else—that has a circular, equatorial orbit:

θ = maximum angle between horizon and satellite

L = latitude of observer

a = satellite semimajor axis (any unit so long as r is the same)

r = radius of planet

As a final note, we may want to talk about how light sources in the sky affect ambient light conditions on a planet’s surface; i.e., how “well-lit” the ground will appear. For this, we can return to measures on insolation. At the equator at midday during the equinox, the sun is delivering about 1360 W/m² to the top of the atmosphere and on a clear day 1050 W/m² will make it to the surface without being scattered away, but if we include light that is scattered but still makes it to the surface then we can raise that value to 1120 W/m².

That’s for a surface directly facing the sun. As a surface is angled to the sun, the light is spread over a greater area, reducing the insolation at any one spot (the sunlight also has to pass through more of the atmosphere, increasing the amount scattered). Walk just 30° north or south of the equator—or sit still and wait for 2 hours—and insolation will be halved, even though to our eyes it still appears perfectly bright. Again, this comes back to the logarithmic nature of our perception of light (and adjustment of sensitivity by dilating and contracting the pupil). An overcast day can have less than 1/10 the insolation of a sunny day and still appear decently lit.

We could describe all light delivered in terms of power per area like this, but by convention it’s often described in terms of illuminance, which is measured in lux, a unit attuned to the specific spectrum of human vision. 1 W/m² of just visible light is equivalent to 683 lx, but no light source is that efficient; for sunlight on Earth the ratio is only 93 lx/(W/m²). That means our ideal clear midday equinox at the equator experiences about 100,000 lx at the surface, but it can drop to 1/4 in the shade. By sunset even lit areas drop to a few hundred lx, and at twilight to 3 lx. A clear night with a full moon can have around 0.05-0.3 lx, and a moonless, overcast sky with no nearby light sources can drop to 0.0001 lx.

Artificial lighting falls surprisingly low on this scale. A typical office space with only artificial lighting has around 3-500 lx, and in homes and hallways it can be as low as 50 lx. Streetlights will typically deliver around 5 lx to the sidewalk.

Given all this, we can state as a rule of thumb that about 1/1,000 the light delivered to a surface directly facing sunlight on Earth’s surface (50 lx) could still be considered well-lit, and 1/1,000 of that (0.05 lx) is still marginally visible, at least by human standards. Now, accounting for the specific lux delivered to a surface by a specific star through a specific atmosphere is a devilishly complicated task, so perhaps it’s simpler to just compare the effect of distance from the star on irradiance, the total light delivered to the top of the atmosphere without accounting for human perception: 

 

 

I = irradiance (relative to Earth)

L = luminosity of light source (relative to sun)

d = distance from light source (AU)

For multiple light sources that illuminate the same side of an object, the irradiances can be independently calculated and added together. If you have a star with a different spectrum from the sun, multiplying this value by 10^{(bolometric correction)/2.5} should roughly reflect how it would appear to a human or organism with similar color and light intensity perception.

Based on these estimates, objects as far as Neptune, 30 AU from the sun, should appear reasonably well-lit, and objects in the Oort cloud as far as 1000 AU away should remain visible from up close—though in reality it will depend on their albedo.

But if the luminosity of the light source is not known—e.g. if it is a planet or moon reflecting light from elsewhere—than illuminance on a surface directly facing that object can be calculated from its apparent magnitude: 

 

 

E_v = illuminance (lx)

M = apparent magnitude

This means that a body directly overhead with an apparent magnitude of -18.3 is sufficient to keep a surface well-lit on its own and -11 is the threshold for a surface to be marginally visible.

D. Aguilar/Harvard-Smithsonian Center for Astrophysics

Calling in the Magratheans

Bearing all the possibilities in mind, I’ve put together a system of plausible planets for Teacup A. Like I said last time, the idea is to get something that resembles our solar system, but with a few interesting choices—some of which won’t quite make sense until the next post. (Note that I first decided on the gas giant radii before finding planetsynth; based on that program they imply fairly low metallicities but are still plausible, so I've kept them.)

Silhouettes of planets (left to right in order of distance from star) and moons over 0.01 Earth radii (down in order of distance from planet) in the Teacup A system, with sizes but not separation to scale.

Teacup Ab (m = 0.1 Earth masses, r = 0.46 Earth radii) is a Mercury analog, though slightly larger and less dense (it’s still the densest planet in the system). Its orbital period is only 20.46 Earth days but, being tidal-locked with low obliquity and eccentricity, this causes little change to its surface. Its dayside is a sweltering hellscape reaching over 800 K, but its nightside remains below freezing and, thanks to delivery of ice by comets, has a permanent icecap. Given that the other planets seem to be acting to continuously pump up its eccentricity, it probably experiences a good deal of tidal heating and may experience occasional bursts of volcanism, so much of the dayside is covered in flood basalts with some impact-generated regolith, and overall it isn’t as cratered as Mercury. I was tempted to move this planet further in and make a lava-ice world, but I wasn’t sure how the clouds of escaping atmosphere might affect sunlight levels further out in the solar system (plus it would make those simulations with Orbe in the last post painfully slow). Perhaps I’ll come back to the idea another time.

Teacup Ac (m = 0.5, r = 0.87) is a dry desert planet with a fairly thin but significant N₂ atmosphere. Though close enough to be tidal-locked, due to its eccentricity of 0.15 it has a 3:2 spin-orbit resonance, meaning a synodic day is twice the length of the year; 27.29 Earth days. It also has a small obliquity of 5°, which in combination with its resonance means that there are small regions near each pole that experience direct sunlight only briefly during their respective summers, and some deep valleys that never experience direct sunlight at all. What little surface moisture the planet has will gather in ice caps here, which will spread outwards and melt near the edges. So even though most of the planet is sweltering hot—over 400K near the equator in midday—there are small temperate regions with liquid surface water. Like Mars there are regions of flood basalt and iron oxide dust, but the planet had a wetter period in its distant past when it formed some andesite that has since eroded into lighter-colored silica dust. There are also some salt flats from former lake basins, though many have been covered by lava flows since then.

Teacup Ad (m = 1.6, r = 1.44) is a super-Earth waterworld, about a quarter water by mass. The ocean is underlain by high-pressure ice and covered by a thick H₂O/N₂ atmosphere. Days are around 130 hours long, which means there are permanent cloud formations that somewhat cool the planet, though a strong greenhouse effect keeps the ocean surface close to boiling. The planet is continuously losing mass to space, and has already lost a significant portion of its oceans.

Teacup Ad I (m = 0.03, r = 0.35) is mutually tidally locked to Ad—the month and days of both bodies are all the same length. Tidal forces help spur occasional volcanism, and much of the surface is covered in flood basalts, but the planet is just about too small to hold onto more than a tenuous CO₂ atmosphere. The planet and moon both do decent jobs of lighting each other during their respective nights; Ad has a diameter of 5.7° and a magnitude of -19.8 as seen from Ad I at midnight (with no eclipse), giving it 177 lx of illumination. Eclipses are also common close to the planet’s equinox, lasting up to 2 hours at any one spot on Ad I.

Teacup Ae (m = 0.8, r = 0.96) is our Earth analog. Its surface is a mix of water oceans, vegetated continents, and polar icecaps, and it has a 2 bar N₂/O₂ atmosphere. It has a somewhat smaller metallic core than Earth—25% the total mass—which gives it a lower density and surface gravity 86% that of Earth. Combined with the thicker atmosphere, this should make flight and eventually space travel easier. Naturally we’ll be spending a lot of time with this planet, so I won’t say much more now.

Teacup Ae I (m  = 1.7*10^-10, r = 0.00084) is a small captured asteroid, similar in size and composition to Mars’s moon Deimos. It’s mostly rock, but contains some internal voids and pockets of ice. From the surface of Ae it looks similar to a planet or satellite seen from Earth, but its speed and direction should make it stand out.

Teacup Ae II (m = 0.004, r = 0.18) is a rough analog to Earth’s moon, with a surface of dark regolith and flood basalts. It has a similar apparent diameter and magnitude to our moon, but because Teacup A appears larger than our sun at this distance, Ae never experiences a total eclipse.

Teacup Af (m = 120, r = 9.64) is a Saturn analog of 0.38 Jupiter masses. Its mass should put it near the peak size a cool gas giant can achieve, but I’ve shrunk it down a little to reflect its temperature and age. Given its equilibrium temperature and some internal heating,  we’ll say it has white bands of water clouds near its equator transitioning to more Jupiter-like red and orange bands towards the poles..

Teacup Af I (m = 0.00005, r = 0.041), III (m = 0.0004, r = 0.084), and IV (m = 0.00015, r = 0.061) are all small rocky moons.

Teacup Af II (m = 0.000009, r = 0.021) is an unusually dense body, 60% metallic by mass, as the result of some collision long ago.

Teacup Af V (m = 0.2, r = 0.65) is the largest moon in the system, with properties broadly similar to Mars with a rusty red exterior, though it’s colder and has a somewhat thicker CO­₂ atmosphere.

Teacup Ag (m = 0.0001, r = 0.061) is a small Ceres analog, the largest body in an asteroid belt nestled between the system’s 2 largest giants. Like Ceres, Ag  formed when its orbit was inside the iceline, and today it remains 20% ice with a thin covering of dust. The interior isn’t fully differentiated and produces too little heat to cause anything more dramatic than occasional cryovolcanism.

Teacup Ah (m = 400, r = 11.10) is the system’s most massive and largest planet. It receives similar sunlight to Saturn, and so has a similar, large beige exterior, though distinct weather bands can be seen on close inspection.

Teacup Ah I (m = 10^-7, r = 0.0078) and II (m = 10^-8, r = 0.0037) are both primarily irregularly-shaped icy bodies, held together by cohesion more than gravity.

Teacup Ah III (m = 0.025, r = 0.33) is our Io analogue, though a big larger. Tidal heating from Ah causes constant, widespread volcanism, giving it a yellow sulfur exterior.

Teacup Ah IV (m = 0.02, r = 0.33) is our Europa analogue with a rocky interior, icy surface, and subsurface water ocean and cryovolcanism thanks to tidal heating.

Teacup Ah V (m = 0.03, r = 0.41) is our Titan analogue, with a Nitrogen atmosphere and methane oceans on its icy crust.

Teacup Ah VI (m = 0.005, r = 0.25) and VII (m = 0.0008, r = 0.15), the trojan moons, are both small, icy bodies.

Teacup Ai (m = 3, r = 1.82) is half water and other volatiles by mass, and has a substantial subsurface water ocean under an icy surface tinted pink by methane and colored by regions of cryovolcanism and cryolava flows. It has a substantial hydrogen atmosphere, and I'll give it some nitrogen lakes at the equator and seasonally at the poles (I didn't do this when I first wrote this post but on reanalysis I think it's appropriate if we assume 10-20 K of greenhouse heating).

Teacup Ai I (m = 0.0001, r = 0.078), II (m = 0.001, r = 0.16), and III (m = 0.0003, r = 0.11) are all icy moons with no particularly unusual features to report just now.

Teacup Aj (m = 25, r = 4.48) is our Neptune analog, a blue ice giant out at the edge of the system. Though in reality it’s about twice as far from Teacup A as the point with equivalent sunlight as Neptune.

Teacup Aj I (m = 0.00002, r = 0.046), II (m = 0.0006, r = 0.14), and IV (m = 0.00005, r = 0.058) are, again, typical icy moons.

Teacup Aj III (m = 0.01, r = 0.33) is a bit larger and has a subsurface ocean.

To round things off, Here are the peak apparent diameters and magnitudes of many of these objects to astronomers on Ae (in visual light):

Body	A	Ad	Ae I	Ae II	Af	Ah	Aj	B
Apparent Diameter	0.78	0.06	0.01	0.54	0.10	0.015	0.001	0.001
Apparent Magnitude	-25.9	-5.0	-3.4	-12.4	-8.4	-0.35	8.2	-9.4

This has a couple interesting implications for astronomers on Ae: At ideal points, The nearest planets will appear large enough to pick out some surface features, in particular the climate bands on Af, and their change in apparent size throughout the year will be obvious. Af and Teacup B will both shine brighter in Ae’s sky than any star in ours. Presuming human-like eyes, Ah will be dim but visible, Ag (apparent magnitude of 5.7) and Ai (apparent magnitude of 6.2) might be just on the cusp of visibility, and Aj will pass unnoticed before telescopes. Af V (apparent magnitude of -2.2) should also appear as a distinct object, as much as 2° apart from Af, so that could help head off any ideas that objects orbit only around Ae.

Relative apparent sizes of objects (and separation of Af and AfV to scale) from the surface of Earth or Teacup Ae. To see how they'd actually appear, back up or zoom out the page until Teacup A is about the size of the nail of your outstretched pinky finger.

 

As a final little note, since first writing up this post, the creator of Stellar System Creator has worked a lot of the math into their program, and you can use it to make some neat renders of your planets; here's one I worked up of Teacup A (just using the default planet textures, but you can pretty easily import a wider variety).

 

In Summary

• A planet's radius can be estimated from its mass in various ways depending on the type of planet.
• Rough estimates can be made from mass alone based on the like composition for planets of Earth-like, Neptune-like, or Jupiter-like masses.
• For rocky worlds and cool waterworlds, it can be estimated from mass and composition.
• For post-runaway waterworlds, it can be estimated from mass, composition, and temperature.
• For gas giants, it can be estimated from mass, composition, insolation, and age.
• Planetary surface temperature depends on a balance between incoming light and outgoing heat, with factors like surface albedo and planetary greenhouse effects altering the rate of absorption and emission.
• Solid planetary surfaces should usually be rocky or icy, but various other more unusual surfaces are plausible.
• Planetary atmospheres are controlled by balances of sources (outgassing, chemistry) and sinks (sequestration, escape), and may evolve significantly over a planet's history.
• Thermal escape, controlled by a planet's escape velocity and temperature and a gas's molar mass, is one of the the main limitations on atmospheric composition.
• Larger planets should have thicker atmospheres as a general trend but individual planets could greatly vary.
• Surface oceans require appropriate temperature and pressure conditions between a liquid's triple point and critical point.
• Apparent brightness to human eyes falls much more slowly than actual sunlight in the outer solar system.
• Daily lunar eclipses, interplanetary eclipses, and reflected-light days are all possible on other bodies.

Notes

Apparently the dynamics of tidal heating were first described by George Darwin, Charles’ grandson.

I find it super amusing that carbon planets sound so valuable to us now, but by the time we have the technology to get to them both diamonds and oil will probably cost peanuts to artificially produce.

Okay, an explanation of the "centrifugal forces are fake" thing if anyone needs it: Physicists will sometimes refer to centrifugal forces as fictitious forces because, if you were observing a rotating system from afar in an inertial reference frame (meaning you are not accelerating in any way) and you described that system in your reference frame, you wouldn't see any centrifugal forces: instead you'd see that objects tend to move in straight lines, and getting them to rotate in a circle requires a continuous centripetal force that pulls inwards towards the axis of rotation (for planets, this is gravity).

However, you can mathematically describe that system with a rotating reference frame, where you assume that everything is moving in a circle and only describe motion relative to that frame; in that case, there are no centripetal forces, but instead there appear to be centrifugal forces pulling everything outwards away from the axis of rotation—because the straight path objects within the rotating system would follow under inertia alone would take them away from the central axis, the inward centripetal force is required to keep them rotating in a circle, and by Newton's 3rd law there must be an equal and opposite outward force in turn. 

There are some issues with this non-inertial reference frame; distant objects not rotating with the system will appear to behave in impossible ways and even in the system odd behavior can appear like the Coriolis effect. But if you're aware of the limits of your framework, account for the odd behavior where you can, and care only about the behavior of objects within the rotating system, these aren't huge problems; a description of centrifugal forces can be used to accurately predict how objects behave on the rotating surface of a planet, and do so a lot easier than having to describe everything in an inertial frame and deal with constant changes in the direction of gravitational and centripetal forces.

Physicist will describe systems with these sorts of convenient if imperfect reference frames all the time. And, according to general relativity, gravity is also a fictitious that appears in reference frames that don't account for the curved geometry of 4-dimensional spacetime. Presuming we don't want to pull out Einstein's field equations to answer simple questions about the motion of objects near planets, I think we're fine using fictitious forces where they produce reasonably accurate predictions.

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Part IVc

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